For Class 8, 9 & 10
Master the basics - and everything after gets easier
Concept-first questions with clear model answers in Physics, Chemistry, Maths and Biology, all NCERT-aligned. Start early, build the habit, and walk into your boards, NEET and JEE already ahead.
Interactive lessons
learn by playingDrag, slide and build - watch each concept come alive, then reveal the answer.
200 interactive lessons
Ohm's law
Class 10 Physics
Slide V & R, watch the bulb glow
Open →pH scale
Class 10 Chemistry
Slide across acids and bases
Open →Atomic number and mass number
Class 9 Chemistry
Add protons & neutrons, build shells
Open →Laws of reflection
Class 8 Physics
Change the angle, watch it bounce
Open →Volume of a sphere
Class 9 Maths
Grow the radius, see the volume
Open →Area of a trapezium
Class 8 Maths
Drag the sides, read the area
Open →Power of a lens
Class 10 Physics
Move the object, trace the rays
Open →Food chain and energy flow
Class 10 Biology
Follow the energy as it flows
Open →Speed
Class 8 Physics
Slide distance & time, watch the speed
Open →Density
Class 9 Physics
Pack mass into volume, float or sink
Open →Work done
Class 9 Physics
Push harder or farther, watch work grow
Open →Kinetic energy
Class 9 Physics
Speed it up - energy grows with the square
Open →Power of a lens
Class 10 Physics
Shorten the focal length, boost the power
Open →Mole concept
Class 9 Chemistry
Weigh out grams, count the moles
Open →Avogadro's number
Class 9 Chemistry
Add moles, count the particles
Open →Microscope magnification
Class 8 Biology
Grow the image, read the magnification
Open →Population density
Class 10 Biology
Add individuals, shrink the land, see crowding
Open →Simple interest
Class 8 Maths
Slide money, rate & time, watch interest
Open →Pythagoras theorem
Class 9 Maths
Stretch the two sides, get the hypotenuse
Open →Probability of an event
Class 10 Maths
Change the outcomes, watch the odds
Open →Newton's second law
Class 9 Physics
Push a mass, pick an acceleration
Open →Momentum
Class 9 Physics
Slide mass & velocity, build momentum
Open →Pressure
Class 8 Physics
Shrink the area, feel the pressure rise
Open →Weight
Class 9 Physics
Change the planet's gravity, watch your weight
Open →Refractive index
Class 10 Physics
Slow light in the medium, raise the index
Open →Resistors in series
Class 10 Physics
Add two resistors in a line
Open →Mass percentage of a solution
Class 9 Chemistry
Dissolve solute, read the strength
Open →Concentration of a solution
Class 9 Chemistry
Pack solute into less liquid
Open →Population change
Class 10 Biology
Balance births against deaths
Open →Compound microscope
Class 8 Biology
Combine eyepiece & objective lenses
Open →Area of a circle
Class 8 Maths
Grow the radius, watch the area square
Open →Volume of a cuboid
Class 8 Maths
Stretch length, breadth & height
Open →Electronic configuration and valency
Class 9 Chemistry
Slide the atomic number, build the atom
Open →Homologous series (alkanes)
Class 10 Chemistry
Add carbons, name the compound
Open →Mass number
Class 9 Chemistry
Add protons & neutrons, get the mass number
Open →Power
Class 9 Physics
More work in less time = more power
Open →Potential energy
Class 9 Physics
Lift a mass higher, store energy
Open →Wave speed
Class 9 Physics
Tune frequency & wavelength, set the speed
Open →Electric current
Class 10 Physics
Push charge per second, get the current
Open →Percentage
Class 8 Maths
Compare part to whole as a %
Open →Electron dot structure
Class 9 Chemistry
Draw valence electrons as dots
Open →Acceleration
Class 9 Physics
Speed up over time, find acceleration
Open →Distance, speed and time
Class 8 Physics
Set speed & time, cover the distance
Open →Frequency and time period
Class 9 Physics
Shorten the period, raise the frequency
Open →Heating effect of current
Class 10 Physics
Raise the current, watch heating soar
Open →Area of a triangle
Class 8 Maths
Set base & height, halve the rectangle
Open →Area of a rectangle
Class 8 Maths
Set length & breadth, fill the area
Open →Mean (average)
Class 9 Maths
Share the total equally across items
Open →Discount
Class 8 Maths
Slide price & % off, see the saving
Open →Heart rate
Class 10 Biology
Set heart rate & time, count the beats
Open →Resistors in parallel
Class 10 Physics
Wire two resistors side by side
Open →Electric charge
Class 10 Physics
Flow current over time, collect charge
Open →Electrical energy and units
Class 10 Physics
Run appliances, add up the units
Open →Kelvin temperature scale
Class 9 Chemistry
Slide Celsius, read the Kelvin
Open →Moles from number of particles
Class 9 Chemistry
Divide particles by Avogadro's number
Open →Ten percent law
Class 10 Biology
See 10% of energy reach the next level
Open →Area of a square
Class 8 Maths
Grow the side, square the area
Open →Volume of a cube
Class 8 Maths
Grow the edge, cube the volume
Open →Circumference of a circle
Class 8 Maths
Grow the radius, roll out the rim
Open →Surface area of a cube
Class 9 Maths
Grow the edge, cover six faces
Open →Potential difference
Class 10 Physics
Share work across charge, get volts
Open →Resistance from Ohm's law
Class 10 Physics
Divide voltage by current, get resistance
Open →Echo and SONAR
Class 9 Physics
Time the echo, find the distance
Open →Mass from moles
Class 9 Chemistry
Multiply moles by molar mass
Open →Breathing rate
Class 10 Biology
Set breathing rate & time
Open →Volume of a cylinder
Class 10 Maths
Set radius & height, fill the can
Open →Compound interest
Class 8 Maths
Compound money over years
Open →Profit and loss percentage
Class 8 Maths
Set cost & selling price, see profit %
Open →Perimeter of a rectangle
Class 8 Maths
Set length & breadth, walk the border
Open →Surface area of a sphere
Class 10 Maths
Grow the radius, wrap the ball
Open →Time period
Class 9 Physics
Raise the frequency, shrink the period
Open →Relative velocity
Class 9 Physics
Two objects approach - add their speeds
Open →Average velocity
Class 9 Physics
Average the start and end speeds
Open →Equations of motion (v = u + at)
Class 9 Physics
Accelerate from u for a time t
Open →Kelvin to Celsius
Class 9 Chemistry
Slide Kelvin, read the Celsius
Open →Population growth rate
Class 10 Biology
Balance births vs deaths per population
Open →Perimeter of a square
Class 8 Maths
Grow the side, walk four edges
Open →Perimeter of a triangle
Class 8 Maths
Add the three sides
Open →Area of a parallelogram
Class 8 Maths
Set base & height, slide the shape
Open →Area of a rhombus
Class 8 Maths
Set the two diagonals
Open →Equations of motion (distance)
Class 9 Physics
Start, accelerate, cover ground
Open →Joule's law of heating
Class 10 Physics
Raise current, resistance or time
Open →Electric power (P = VI)
Class 10 Physics
Multiply voltage by current
Open →Average atomic mass of isotopes
Class 9 Chemistry
Mix two isotopes by abundance
Open →Seed germination percentage
Class 9 Biology
Count sprouted seeds out of the total
Open →Volume of a cone
Class 9 Maths
Set radius & height, fill the cone
Open →Surface area of a cylinder
Class 9 Maths
Wrap the side and both ends
Open →Surface area of a cuboid
Class 9 Maths
Cover all six rectangular faces
Open →nth term of an AP
Class 10 Maths
Step from the first term by d
Open →Sum of an AP
Class 10 Maths
Add up the first n terms
Open →Focal length of a mirror
Class 10 Physics
Halve the radius to find the focus
Open →Speed of light in a medium
Class 10 Physics
Raise the index, slow the light
Open →Percentage purity
Class 9 Chemistry
Weigh the pure part of a sample
Open →Slope of a line
Class 10 Maths
Rise over run gives the steepness
Open →Percentage change
Class 8 Maths
Compare a new value to the old
Open →Volume of a hemisphere
Class 9 Maths
Grow the radius of half a ball
Open →Area of a sector
Class 10 Maths
Cut a slice of angle from a circle
Open →Length of an arc
Class 10 Maths
Measure the curved edge of a slice
Open →Slant height of a cone
Class 9 Maths
Combine radius & height for the slant
Open →Unit conversion (km/h to m/s)
Class 9 Physics
Convert km/h into m/s
Open →Equations of motion (v^2 = u^2 + 2as)
Class 9 Physics
Accelerate over a distance, find v
Open →Impulse
Class 9 Physics
Hit harder or longer, change momentum
Open →Wavelength
Class 9 Physics
Speed over frequency gives wavelength
Open →Oscillations
Class 9 Physics
Vibrate at a frequency for a time
Open →Cost of electricity
Class 10 Physics
Units times rate gives the bill
Open →Number of neutrons
Class 9 Chemistry
Take protons away from the mass number
Open →Curved surface area of a cone
Class 9 Maths
Wrap the slanted side of a cone
Open →Total surface area of a cone
Class 9 Maths
Add the base circle to the cone's side
Open →Curved surface area of a hemisphere
Class 9 Maths
Cover the dome of a hemisphere
Open →Diagonal of a square
Class 9 Maths
Cross a square corner to corner
Open →Unit conversion (m/s to km/h)
Class 9 Physics
Convert m/s into km/h
Open →Distance from velocities
Class 9 Physics
From two speeds, find the distance
Open →Diagonal of a rectangle
Class 9 Maths
Cross a rectangle corner to corner
Open →Diagonal of a cuboid
Class 9 Maths
The longest rod that fits in a box
Open →Area by Heron's formula
Class 9 Maths
Area from just the three sides
Open →Interior angle sum of a polygon
Class 8 Maths
Add up a polygon's inside angles
Open →Exterior angle of a regular polygon
Class 8 Maths
Share 360 among a polygon's corners
Open →Number of diagonals of a polygon
Class 8 Maths
Count the diagonals of a polygon
Open →Discriminant
Class 10 Maths
Test how many roots a quadratic has
Open →Sum of roots
Class 10 Maths
Sum of a quadratic's roots
Open →Punnett square (monohybrid cross)
Class 10 Biology
Cross two parents, predict the offspring
Open →Balancing chemical equations
Class 10 Chemistry
Slide coefficients until atoms balance
Open →Writing chemical formulae (valency)
Class 9 Chemistry
Criss-cross valencies into a formula
Open →Current from power
Class 10 Physics
Divide power by voltage for current
Open →Power (P = V^2 / R)
Class 10 Physics
Voltage squared over resistance
Open →Sine ratio
Class 10 Maths
Opposite over hypotenuse
Open →Cosine ratio
Class 10 Maths
Adjacent over hypotenuse
Open →Tangent ratio
Class 10 Maths
Opposite over adjacent
Open →Area of an equilateral triangle
Class 9 Maths
Area of an equilateral triangle
Open →Curved surface area of a cylinder
Class 9 Maths
Wrap only the curved side
Open →Loss percentage
Class 8 Maths
Sell below cost, find the loss %
Open →Amount with simple interest
Class 8 Maths
Principal plus its simple interest
Open →Distance formula
Class 10 Maths
Straight distance between two points
Open →States of matter
Class 9 Chemistry
Heat particles solid → liquid → gas
Open →Parts of a plant cell
Class 8 Biology
Tap a cell part to see its job
Open →Diagonal of a cube
Class 9 Maths
Longest diagonal through a cube
Open →Total surface area of a hemisphere
Class 9 Maths
Dome plus its flat circle
Open →Sum of first n natural numbers
Class 10 Maths
Add 1 + 2 + ... + n instantly
Open →Range of data
Class 9 Maths
Spread from smallest to largest
Open →Class mark
Class 9 Maths
Midpoint of a class interval
Open →Selling price from profit percent
Class 8 Maths
Mark up cost by a profit %
Open →Perimeter of a sector
Class 10 Maths
Two radii plus the curved arc
Open →Circumference from diameter
Class 8 Maths
Circumference straight from diameter
Open →Power (P = F x v)
Class 9 Physics
Force times velocity gives power
Open →Percentage of a number
Class 8 Maths
Find a percentage of a number
Open →Series and parallel circuits
Class 10 Physics
Break a bulb in series vs parallel
Open →Symbols of elements
Class 9 Chemistry
Match each element to its symbol
Open →Free fall (velocity)
Class 9 Physics
Drop from a height, hit this speed
Open →Free fall (time)
Class 9 Physics
How long a drop takes
Open →Free fall (distance)
Class 9 Physics
Distance fallen in a given time
Open →Complement of an event
Class 10 Maths
Chance an event does NOT happen
Open →Product of roots
Class 10 Maths
Product of a quadratic's roots
Open →Exterior angle theorem
Class 9 Maths
Exterior angle = sum of remote interiors
Open →Complementary angles
Class 10 Maths
What adds to 90 degrees
Open →Supplementary angles
Class 9 Maths
What adds to 180 degrees
Open →Perimeter of a semicircle
Class 10 Maths
Curved half plus the diameter
Open →Area of a semicircle
Class 10 Maths
Half the area of a circle
Open →Turning effect (moments)
Class 9 Physics
Balance the see-saw with moments
Open →Reflex arc
Class 10 Biology
Step through a reflex, stimulus to action
Open →Buoyant force (upthrust)
Class 9 Physics
Displace liquid, feel the upthrust
Open →Relative density
Class 9 Physics
Compare a density to water's
Open →Power in lifting a load
Class 9 Physics
Lift a load, faster needs more power
Open →Cosecant ratio
Class 10 Maths
Hypotenuse over opposite
Open →Secant ratio
Class 10 Maths
Hypotenuse over adjacent
Open →Cotangent ratio
Class 10 Maths
Adjacent over opposite
Open →Height from angle of elevation
Class 10 Maths
Height from an angle of elevation
Open →Area of a quadrant
Class 10 Maths
A quarter of a circle's area
Open →Interior angle of a regular polygon
Class 8 Maths
One inside angle of a regular polygon
Open →Sum of first n odd numbers
Class 10 Maths
Add the first n odd numbers
Open →Sum of first n even numbers
Class 10 Maths
Add the first n even numbers
Open →Quadratic formula (a root)
Class 10 Maths
Larger root of a quadratic
Open →LCM from HCF
Class 10 Maths
LCM from the product and HCF
Open →Depreciation
Class 8 Maths
Value drops by a % each year
Open →Cost price from selling price
Class 8 Maths
Work back to the cost price
Open →Downstream speed
Class 8 Maths
Row with the current
Open →Upstream speed
Class 8 Maths
Row against the current
Open →Average speed for a round trip
Class 8 Maths
Average speed there and back
Open →Sales tax / GST
Class 8 Maths
Tax added on a price
Open →Area of a ring (annulus)
Class 10 Maths
Area of a ring between two circles
Open →Edge of a cube from volume
Class 9 Maths
Edge back from the volume
Open →Radius from area
Class 10 Maths
Radius back from a circle's area
Open →Side from area of a square
Class 8 Maths
Side back from a square's area
Open →Height of a triangle from area
Class 9 Maths
Height back from area and base
Open →Rate from simple interest
Class 8 Maths
Rate back from the interest
Open →Time from simple interest
Class 8 Maths
Time back from the interest
Open →Principal from simple interest
Class 8 Maths
Principal back from the interest
Open →Mean proportional
Class 10 Maths
Geometric mean of two numbers
Open →Fourth proportional
Class 8 Maths
Complete the proportion a : b = c : ?
Open →Marked price from selling price
Class 8 Maths
Marked price back from the sale price
Open →Chambers of the human heart
Class 10 Biology
Tap a heart chamber to see its job
Open →Equation of a line (y = mx + c)
Class 9 Maths
Read y off a straight line
Open →Average term of an AP
Class 10 Maths
Average of first and last term
Open →Number of terms in an AP
Class 10 Maths
How many terms in an AP
Open →Midpoint of two points
Class 10 Maths
x-coordinate of a midpoint
Open →Empirical mode
Class 10 Maths
Estimate the mode from mean & median
Open →Length of a shadow
Class 10 Maths
Shadow from height and sun angle
Open →Train crossing a pole
Class 8 Maths
Speed to cross a pole
Open →Time and work
Class 8 Maths
More workers, fewer days
Open →Dividing in a ratio
Class 8 Maths
Split a total in a ratio
Open →Unitary method
Class 8 Maths
Cost of a single item
Open →Your progress — Foundation - Class 8 to 10
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Showing 17 questions for Class 9. Tap a card to reveal the answer.
PhysicsMotionmediumA car starting from rest accelerates uniformly at 2 m/s^2 for 5 seconds. Find its final velocity and the distance travelled.
Reveal answer ↓
What it is
The three equations of motion connect initial velocity, acceleration, time, distance and final velocity for steady acceleration.
Answer
Given u = 0, a = 2 m/s^2, t = 5 s. Final velocity v = u + at = 0 + 2 x 5 = 10 m/s. Distance s = ut + (1/2)at^2 = 0 + (1/2)(2)(5^2) = 25 m. So the car reaches 10 m/s and covers 25 m.
v = u + at ; s = ut + (1/2)at^2
- •v = u + at = 10 m/s
- •s = ut + (1/2)at^2 = 25 m
- •u = 0 (starts from rest)
Why learn this
They let engineers predict a rocket's speed, a car's braking distance and a ball's flight - the maths of all moving things.
💡 Memory trick
Use 'v = u + at' first (no distance), then 's = ut + 1/2 at^2'. Velocity gets a time-boost 'at'.
PhysicsMotionmediumA body speeds up from 0 to 20 m/s in 5 s. Find its acceleration. Slide the values to explore.
Reveal answer ↓
What it is
Acceleration is the rate at which velocity changes with time.
Answer
Acceleration = (final velocity - initial velocity) / time = (20 - 0) / 5 = 4 m/s^2. If the final velocity is less than the initial velocity the acceleration is negative, which means the body is decelerating (slowing down).
a = (v - u) / t
- •a = (v - u) / t
- •Unit: m/s^2
- •Negative acceleration = deceleration
Why learn this
It tells us how quickly vehicles speed up or slow down.
💡 Memory trick
a = (v - u) / t. A negative answer means slowing down.
PhysicsMotionmediumTwo cars approach each other at 20 m/s and 10 m/s. How fast do they close in? Slide to explore.
Reveal answer ↓
What it is
When two bodies move directly towards each other, their relative speed is the sum of their individual speeds.
Answer
Moving towards each other, the relative speed = u + v = 20 + 10 = 30 m/s. The gap between them shrinks at 30 metres every second - faster than either car alone.
relative speed (approaching) = u + v
- •Towards each other: relative speed = u + v
- •Same direction: relative speed = difference
- •Unit: m/s
Why learn this
It explains how quickly two approaching vehicles or trains actually close in.
💡 Memory trick
Towards each other -> add: relative speed = u + v.
PhysicsMotioneasyA body speeds up from 10 m/s to 30 m/s uniformly. Find its average velocity. Slide to explore.
Reveal answer ↓
What it is
For uniformly accelerated motion, the average velocity is the mean of the initial and final velocities.
Answer
Average velocity = (u + v) / 2 = (10 + 30) / 2 = 20 m/s. This midpoint value works because, under uniform acceleration, the velocity increases at a steady rate.
average velocity = (u + v) / 2
- •Average velocity = (u + v) / 2
- •Valid for uniform acceleration
- •Unit: m/s
Why learn this
It lets us use a single steady speed to work out the distance covered.
💡 Memory trick
Average velocity = (u + v) / 2 - the midpoint speed.
PhysicsMotionmediumA body starts at 5 m/s and accelerates at 2 m/s^2 for 5 s. Find its final velocity. Slide to explore.
Reveal answer ↓
What it is
The first equation of motion gives the final velocity as the initial velocity plus acceleration times time.
Answer
Final velocity v = u + a t = 5 + 2 x 5 = 5 + 10 = 15 m/s. The term a t is the extra velocity gained during the time t at constant acceleration.
v = u + a t
- •v = u + a t
- •a t is the velocity gained
- •Valid for constant acceleration
Why learn this
It predicts how fast something is going after accelerating for a while.
💡 Memory trick
v = u + a t. Start speed plus the speed gained.
PhysicsMotionmediumA body starts at 10 m/s and accelerates at 2 m/s^2 for 5 s. How far does it go? Slide to explore.
Reveal answer ↓
What it is
The second equation of motion gives the distance covered under uniform acceleration.
Answer
Distance s = u t + 1/2 a t^2 = 10 x 5 + 1/2 x 2 x 5^2 = 50 + 25 = 75 metres. The first term (u t) is the distance at the starting speed; the second term is the extra distance from accelerating.
s = u t + 1/2 a t^2
- •s = u t + 1/2 a t^2
- •u t is steady travel, 1/2 a t^2 is the extra
- •Valid for uniform acceleration
Why learn this
It predicts how far a body travels while it is speeding up.
💡 Memory trick
s = u t + 1/2 a t^2. Steady part plus the accelerating part.
PhysicsMotioneasyConvert 72 km/h into metres per second. Slide the speed to explore.
Reveal answer ↓
What it is
To convert a speed from kilometres per hour to metres per second, multiply by 5 and divide by 18.
Answer
m/s = km/h x 5 / 18 = 72 x 5 / 18 = 360 / 18 = 20 m/s. The factor 5/18 comes from 1000 metres in a kilometre divided by 3600 seconds in an hour.
m/s = km/h x 5 / 18
- •m/s = km/h x 5 / 18
- •5/18 = 1000 / 3600
- •To go back, multiply m/s by 18/5
Why learn this
Physics numericals use m/s, but everyday speeds are quoted in km/h.
💡 Memory trick
m/s = km/h x 5 / 18. (1000 m in 3600 s.)
PhysicsMotionmediumA body starts at 10 m/s and accelerates at 2 m/s^2 over 100 m. Find its final velocity. Slide to explore.
Reveal answer ↓
What it is
The third equation of motion links the final velocity to the distance travelled under uniform acceleration.
Answer
Using v^2 = u^2 + 2as = 10^2 + 2 x 2 x 100 = 100 + 400 = 500, so v = sqrt(500) = 22.36 m/s. This equation is handy because it connects velocity and distance directly, without the time.
v^2 = u^2 + 2as
- •v^2 = u^2 + 2as
- •Uses distance, not time
- •v = sqrt(u^2 + 2as)
Why learn this
It finds the final speed when the time is not known - only the distance.
💡 Memory trick
v^2 = u^2 + 2as. No time needed - it uses distance instead.
PhysicsMotioneasyConvert 20 m/s into kilometres per hour. Slide the speed to explore.
Reveal answer ↓
What it is
To convert a speed from metres per second to kilometres per hour, multiply by 18 and divide by 5.
Answer
km/h = m/s x 18 / 5 = 20 x 18 / 5 = 360 / 5 = 72 km/h. This is the reverse of the km/h to m/s rule, which multiplies by 5/18.
km/h = m/s x 18 / 5
- •km/h = m/s x 18 / 5
- •Reverse of x 5/18
- •20 m/s = 72 km/h
Why learn this
It turns a physics answer in m/s back into the km/h we see on road signs.
💡 Memory trick
km/h = m/s x 18 / 5 (the reverse of x 5/18).
PhysicsMotionmediumA body goes from 10 m/s to 30 m/s at 2 m/s^2. Find the distance covered. Slide to explore.
Reveal answer ↓
What it is
The distance covered can be found from the initial and final velocities and the acceleration.
Answer
Distance s = (v^2 - u^2) / (2a) = (30^2 - 10^2) / (2 x 2) = (900 - 100) / 4 = 800 / 4 = 200 m. This is the third equation of motion rearranged to make the distance the subject.
s = (v^2 - u^2) / (2a)
- •s = (v^2 - u^2) / (2a)
- •Rearranged from v^2 = u^2 + 2as
- •No time needed
Why learn this
It gives the stopping or run-up distance when only the speeds and acceleration are known.
💡 Memory trick
s = (v^2 - u^2) / (2a), from v^2 = u^2 + 2as.
PhysicsMotioneasyDifferentiate between distance and displacement.
Reveal answer ↓
What it is
Distance is the total path length covered; displacement is the shortest straight-line distance from start to finish, with direction.
Answer
Distance is the actual length of the path travelled by a body, irrespective of direction; it is a scalar quantity and is always positive. Displacement is the shortest distance measured from the initial to the final position of the body in a particular direction; it is a vector quantity and can be positive, negative or zero. Distance is always greater than or equal to the magnitude of displacement.
Displacement = shortest distance (with direction)
- •Distance: total path length, scalar
- •Displacement: shortest path with direction, vector
- •Displacement can be zero
- •Distance >= magnitude of displacement
Why learn this
It explains why an athlete running one full round of a track covers distance but has zero displacement.
💡 Memory trick
Distance = scalar (only size). Displacement = vector (size + direction), can be zero.
PhysicsMotioneasyDefine speed and velocity. State their SI unit.
Reveal answer ↓
What it is
Speed is the rate of change of distance; velocity is the rate of change of displacement, so it has direction.
Answer
Speed is the distance travelled by a body per unit time; it is a scalar quantity. Velocity is the displacement of a body per unit time in a given direction; it is a vector quantity. The SI unit of both speed and velocity is the metre per second (m/s).
Speed = distance/time ; Velocity = displacement/time
- •Speed = distance / time (scalar)
- •Velocity = displacement / time (vector)
- •SI unit m/s
- •Velocity has direction
Why learn this
Velocity, not just speed, is needed to describe motion fully (e.g. a car turning).
💡 Memory trick
Speed = scalar (how fast). Velocity = vector (how fast AND which way).
PhysicsMotionmediumA car's velocity increases from 10 m/s to 30 m/s in 5 s. Find its acceleration.
Reveal answer ↓
What it is
Acceleration is the rate of change of velocity with time.
Answer
Acceleration a = (final velocity - initial velocity) / time = (v - u)/t = (30 - 10)/5 = 20/5 = 4 m/s^2. So the car accelerates at 4 metres per second squared.
a = (v - u) / t
- •a = (v - u)/t
- •(30 - 10)/5 = 4
- •SI unit m/s^2
- •Negative value means retardation
Why learn this
It tells how quickly a vehicle speeds up or slows down.
💡 Memory trick
Acceleration = change in velocity / time. Negative acceleration = retardation.
PhysicsMotionmediumWrite the three equations of motion and state what each symbol means.
Reveal answer ↓
What it is
For uniform acceleration, the three equations of motion relate u, v, a, t and s.
Answer
The three equations of motion for uniform acceleration are: v = u + at; s = ut + (1/2)a t^2; and v^2 = u^2 + 2as. Here u is the initial velocity, v is the final velocity, a is the acceleration, t is the time and s is the displacement. They are valid only when the acceleration is uniform (constant).
v = u + at ; s = ut + 1/2 a t^2 ; v^2 = u^2 + 2as
- •v = u + at
- •s = ut + 1/2 a t^2
- •v^2 = u^2 + 2as
- •Valid only for uniform acceleration
Why learn this
They let us predict the position and velocity of a body at any time.
💡 Memory trick
v = u + at ; s = ut + 1/2 a t^2 ; v^2 = u^2 + 2as.
PhysicsMotionmediumA body starting from rest accelerates at 2 m/s^2 for 5 s. Find the distance covered.
Reveal answer ↓
What it is
The equations of motion solve problems where a body moves with uniform acceleration.
Answer
Given u = 0 (starts from rest), a = 2 m/s^2, t = 5 s. Using s = ut + (1/2)a t^2 = 0 x 5 + (1/2)(2)(5^2) = 0 + (1/2)(2)(25) = 25 m. So the body covers 25 metres.
s = ut + 1/2 a t^2
- •u = 0, a = 2, t = 5
- •s = ut + 1/2 a t^2
- •s = 0 + 1/2 x 2 x 25
- •Distance = 25 m
Why learn this
It is how we calculate braking distances and launch speeds.
💡 Memory trick
Pick the equation that has the three known quantities and the one you want to find.
PhysicsMotionmediumWhy is uniform circular motion called accelerated motion?
Reveal answer ↓
What it is
A body moving in a circle at constant speed is accelerating because its direction keeps changing.
Answer
In uniform circular motion, a body moves along a circular path with a constant speed. However, its direction of motion changes continuously at every point. Since velocity depends on both speed and direction, the velocity is changing even though the speed is constant. A changing velocity means the body is accelerating, so uniform circular motion is an accelerated motion.
v = 2 pi r / t (speed in a circle)
- •Constant speed along a circle
- •Direction changes continuously
- •Velocity changes -> acceleration
- •Example: stone tied to a string
Why learn this
It explains why a stone on a string or a satellite keeps turning inward.
💡 Memory trick
Constant speed but changing direction -> velocity changes -> it is accelerated motion.
PhysicsMotionmediumWhat do the slope and the area under a velocity-time graph represent?
Reveal answer ↓
What it is
On a velocity-time graph, the slope gives acceleration and the area under the graph gives displacement.
Answer
On a velocity-time graph, the slope of the line represents the acceleration of the body, since acceleration is the change in velocity per unit time. The area enclosed between the graph line and the time axis represents the distance (displacement) travelled by the body. A straight, slanting line indicates uniform acceleration, while a horizontal line indicates uniform velocity.
Acceleration = slope ; Distance = area under v-t graph
- •Slope of v-t graph = acceleration
- •Area under v-t graph = distance
- •Horizontal line = uniform velocity
- •Slanting line = uniform acceleration
Why learn this
Graphs let us read motion information quickly without formulae.
💡 Memory trick
Slope of v-t graph = acceleration; area under v-t graph = distance travelled.
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