Equations of Motion and Uniform Acceleration
Learn the kinematic equations for uniformly accelerated motion, including applications to free fall, retardation, and calculation of distance in specific time intervals.
Why this shows up in the exam
You need to apply these equations to solve problems involving objects moving with constant acceleration, a frequent NEET topic.
How NEET tests this
Learn the idea
Uniform acceleration means the acceleration stays constant, so the velocity changes linearly and the distance travelled equals the average velocity multiplied by time.
🧠 Memory hook: Distance = average speed × time → average speed is simply (initial + final)/2 for constant acceleration.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v = u + a t
- s = u t + ½ a t²
- s = (u + v) t / 2
- a is constant → velocity‑time graph is a straight line
- Convert km/h to m/s by multiplying by 5/18
How to approach it
- 1List the given quantities and convert them to SI units
- 2Find the missing acceleration or velocity using v = u + a t if needed
- 3Choose the SUVAT formula that contains the known variables and the required distance
- 4Compute s and check the unit
Worked example — watch it click
If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s. Then it covers a distance of:
- A)20 m
- ✅400 m
- C)1440 m
- D)2880 m
The concept behind this problem
The worked example asks for the distance when a car starts from rest and reaches a known speed in a known time, exactly the situation where s = (u+v) t /2 or s = ½ a t² applies.
Step by step
- 1Final velocity = 144 km/h = 144×(5/18) = 40 m/s.
- 2Initial velocity u = 0, t = 20 s.
- 3Using s = ut + (1/2)at²: First find a = (v-u)/t = 40/20 = 2 m/s².
- 4Then s = 0 + (1/2)(2)(20²) = 400 m.
- 5Or use s = (u+v)t/2 = (0+40)×20/2 = 400 m.
Watch out
Students often multiply the final speed (40 m/s) by the time (20 s) and get 800 m, forgetting that the speed was not constant.
Common slip-ups that cost marks
- •Using final speed directly as distance = v·t (ignores that speed is not constant)
- •Forgetting to convert km/h to m/s before using the equations
- •Mixing up sign of acceleration when the motion is retardation
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Practise it
These are real questions from past NEET papers that test this exact idea.
If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s. Then it covers a distance of:
Push further
More challenging4 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.
A particle moves such that its velocity is given by v(x) = P/x + Q, where P and Q are constants and x is the position. Find the acceleration of the particle as a function of x.
More from Kinematics
Distance, Displacement, Speed, and Velocity
Understand the differences between distance and displacement, and between speed and velocity, including how to calculate average speed and average velocity in various scenarios.
Projectile Motion
Study the motion of projectiles, including the independence of horizontal and vertical components, trajectory equations, maximum height, and the effect of initial conditions.
Relative Velocity and Motion Analysis
Explore how to determine the velocity of one object relative to another and analyze motion from different reference frames, including periodic motion.
Position, Path Length, and Displacement
For one-dimensional motion, displacement over an interval is Delta x = x_f - x_i and may be positive, negative, or zero. Distance is the non-negative path length, so distance is always at least |Delta x|.
Speed and Velocity
Instantaneous velocity is the signed rate v = dx/dt, while instantaneous speed is |v|. In one dimension the sign of v identifies motion along or opposite the positive axis.
Average Speed and Average Velocity
Over elapsed time Delta t, average speed equals total distance/Delta t and average velocity equals Delta x/Delta t. For equal distances the relevant mean of speeds is harmonic, not arithmetic.