Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
A frequent error is confusing average velocity (total displacement/total time) with instantaneous velocity. In reality, the velocity at a single instant — the slope of the position–time graph at that point.
Memory trick: read it as the tangent slope of the x–t graph.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
The rate of change of velocity; it is a vector, so direction matters.
Memory trick: a body can have zero velocity yet non-zero acceleration.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
A frequent error is assuming acceleration is zero whenever velocity is zero (e.g. at the top of a throw, v=0 but a=−g). In reality, the rate of change of velocity; it is a vector, so direction matters.
Memory trick: a body can have zero velocity yet non-zero acceleration.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
The v=u+at family that connects u, v, a, s and t — valid only for constant acceleration.
Memory trick: if a is not constant, you must use calculus, not these three equations.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
A frequent error is using them when acceleration is changing. In reality, the v=u+at family that connects u, v, a, s and t — valid only for constant acceleration.
Memory trick: if a is not constant, you must use calculus, not these three equations.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
Motion under gravity where horizontal and vertical motions are independent — horizontal a=0, vertical a=−g.
Memory trick: split every projectile into a horizontal (constant-velocity) and vertical (free-fall) problem.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
A frequent error is applying v=u+at to the whole velocity instead of resolving into x and y components. In reality, motion under gravity where horizontal and vertical motions are independent — horizontal a=0, vertical a=−g.
Memory trick: split every projectile into a horizontal (constant-velocity) and vertical (free-fall) problem.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
A frequent error is adding speeds as plain numbers instead of subtracting vectors. In reality, the velocity of A as seen from B equals vector v(A) − v(B).
Memory trick: for opposite directions the relative speed adds; for the same direction it subtracts.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
Final velocity after time t under constant acceleration. Use it when acceleration is constant.
v = u + at
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
Displacement after time t under constant acceleration. Use it when acceleration is constant.
s = ut + ½at²
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
Links velocity and displacement without time. Use it when acceleration is constant.
v² = u² + 2as
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
Horizontal range of a projectile on level ground; maximum at θ=45°. Use it when launch and landing are at the same height.
R = u²sin2θ/g
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
Speed is a scalar (how fast); velocity is a vector (how fast AND in which direction).
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
Average velocity is displacement over a time interval; instantaneous velocity is the value at one exact moment.
“Every time you judge whether to cross before an approaching car, your brain is quietly solving kinematics.”
Pick one sign convention for up/down and keep it for the whole problem.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
The tendency of a body to resist any change in its state of rest or uniform motion (Newton's first law).
Memory trick: force changes motion; it isn't needed to maintain constant velocity.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
A frequent error is thinking a moving body needs a continuous force to keep moving — it doesn't, unless friction acts. In reality, the tendency of a body to resist any change in its state of rest or uniform motion (Newton's first law).
Memory trick: force changes motion; it isn't needed to maintain constant velocity.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
A frequent error is using a single force instead of the net (vector sum) force. In reality, the net force equals mass times acceleration, F=ma, in the direction of the net force.
Memory trick: always draw a free-body diagram and add forces as vectors first.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
A frequent error is thinking action and reaction cancel out — they can't, because they act on different objects. In reality, every action has an equal and opposite reaction, and the two forces act on different bodies.
Memory trick: identify the two different bodies before pairing action–reaction forces.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
Static friction adjusts itself up to a maximum μₛN to prevent motion; kinetic friction μₖN opposes sliding.
Memory trick: friction is a response force; it never exceeds μₛN before slipping.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
A frequent error is assuming friction always equals μN — static friction is only as big as needed, up to its limit. In reality, static friction adjusts itself up to a maximum μₛN to prevent motion; kinetic friction μₖN opposes sliding.
Memory trick: friction is a response force; it never exceeds μₛN before slipping.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
The contact push a surface exerts perpendicular to itself.
Memory trick: on an incline N=mg·cosθ, and it changes if there are extra vertical forces.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
A frequent error is assuming the normal force always equals mg. In reality, the contact push a surface exerts perpendicular to itself.
Memory trick: on an incline N=mg·cosθ, and it changes if there are extra vertical forces.
“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”
The maximum static friction before an object starts to slip. Use it when the object is still stationary.
fₛ(max) = μₛN