Describe motion with position, velocity, and acceleration, and read what a motion graph is actually telling you — most of the formulas here connect the same handful of variables in different combinations. Every question comes with a written walkthrough of which equation applied.
The slope of a position-time graph gives velocity; the slope of a velocity-time graph gives acceleration — using the wrong graph's slope for the wrong quantity is one of the most common errors in kinematics.
An object moving in the negative direction that speeds up has negative acceleration too — whether acceleration speeds an object up or slows it down depends on whether it points in the same direction as the velocity, not on its sign alone.
Each kinematic equation is missing exactly one of the five standard variables — picking the equation that happens to exclude the one unknown variable in the problem saves a step, and picking the wrong equation means solving for a variable you don't have.
Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.
A car accelerates from rest at 4 m/s² for 5 seconds. What is its final velocity?
A — 20 m/s. Using v = v₀ + at, with v₀ = 0: v = 0 + (4)(5) = 20 m/s. 9 m/s (B) comes from adding acceleration and time instead of multiplying them: 4+5=9.
An object is dropped from rest and falls for 3 seconds. Using g = 10 m/s², how far does it fall?
A — 45 m. Using d = v₀t + ½gt², with v₀ = 0: d = ½(10)(3²) = ½(10)(9) = 45 m. 30 m (B) comes from computing g×t (10×3=30) instead of ½gt² — skipping both the squaring and the ½ factor.
A ball is thrown upward with an initial velocity of 20 m/s. Using g = 10 m/s² (acting downward), how long does it take for the ball to reach its maximum height, and what is the maximum height?
A — 2 s; 20 m. At maximum height, vertical velocity equals zero: 0 = 20 − (10)(t), so t = 2 s. Using that time in the displacement equation: d = (20)(2) − ½(10)(2²) = 40 − 20 = 20 m. 2 s; 40 m (B) gets the time right but reports the distance the ball would have traveled if it kept moving at its initial velocity the whole time (20×2=40), without accounting for gravity decelerating it along the way.
Kinematics problems reward matching the right equation to the variables you actually have — once the equation is chosen correctly, the algebra is usually straightforward.
Write out position, initial velocity, final velocity, acceleration, and time, marking which values are given and which are unknown, before selecting an equation. Untimed practice is where that habit sticks.
Move to timed sessions once equation selection is instant.
Pair kinematics with forces and Newton's laws in a mock — most projectile and incline problems combine both.
Already have an account? Sign in →