Circular Motion Equations Worksheet
Practice uniform circular motion with 10 problems covering centripetal acceleration, centripetal force, angular velocity, and period. Full solutions included.
View worksheet →Kinematics Equations Worksheet
Practice the four kinematic equations (SUVAT) with this set of 12 progressively challenging problems. Includes a full worked answer key. Ideal for GCSE, AP Physics 1, and IB Physics students.
Equations you will need
| v = u + at | Final velocity from initial velocity, acceleration, and time |
| s = ut + ½at² | Displacement from initial velocity, time, and acceleration |
| v² = u² + 2as | Final velocity squared (no time needed) |
| s = ½(u + v)t | Displacement from average velocity and time |
Symbol key
| Symbol | Quantity | Unit |
|---|---|---|
| s | displacement | m (metres) |
| u | initial velocity | m/s |
| v | final velocity | m/s |
| a | acceleration | m/s² |
| t | time | s (seconds) |
Practice problems
Attempt each problem on paper first, then click Show answer to check your working.
-
A car accelerates from rest at 3 m/s² for 8 seconds. Find its final velocity.
Show answer
v = u + at = 0 + (3)(8) = 24 m/s -
A cyclist travelling at 5 m/s accelerates uniformly to 15 m/s in 4 seconds. Calculate the acceleration.
Show answer
a = (v - u)/t = (15 - 5)/4 = 2.5 m/s² -
A stone is dropped from a cliff and falls for 3 seconds. How far does it fall? (g = 9.8 m/s²)
Show answer
s = ut + ½at² = 0 + ½(9.8)(3²) = 44.1 m -
A train decelerates from 30 m/s to rest over a distance of 450 m. Find the deceleration.
Show answer
v² = u² + 2as → 0 = 900 + 2a(450) → a = -1 m/s² -
A ball is thrown vertically upward at 20 m/s. How high does it rise? (g = 9.8 m/s²)
Show answer
v² = u² + 2as → 0 = 400 - 2(9.8)s → s = 20.4 m -
A car travels at 25 m/s and brakes uniformly, stopping in 5 seconds. Find the braking distance.
Show answer
s = ½(u+v)t = ½(25+0)(5) = 62.5 m -
An object accelerates from 4 m/s to 12 m/s over 32 m. Find the acceleration.
Show answer
v² = u² + 2as → 144 = 16 + 64a → a = 2 m/s² -
A skydiver falls from rest. After 4 s of free fall, find her velocity. (g = 9.8 m/s²)
Show answer
v = u + at = 0 + 9.8(4) = 39.2 m/s -
A car accelerates from 10 m/s at 2 m/s² for 6 s. Find the distance covered.
Show answer
s = ut + ½at² = 10(6) + ½(2)(36) = 60 + 36 = 96 m -
A rocket reaches 200 m/s from rest with acceleration 8 m/s². Find the time taken.
Show answer
t = (v - u)/a = 200/8 = 25 s -
A ball rolls down a ramp with constant acceleration. It covers 9 m in the first 3 s starting from rest. Find the acceleration.
Show answer
s = ½at² → 9 = ½a(9) → a = 2 m/s² -
A car travels at 20 m/s, then accelerates at 1.5 m/s² for 8 s. Find the final velocity and the total distance.
Show answer
v = 20 + 1.5(8) = 32 m/s; s = 20(8) + ½(1.5)(64) = 160 + 48 = 208 m
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View worksheet →About this worksheet
This kinematics equations worksheet covers the essential equations for mechanics at the GCSE / AP Physics 1 / IB SL level. Every problem has been written to mirror the style and difficulty of real exam questions, with full algebraic working shown in the solutions.
If you find these problems too straightforward, try the more advanced worksheets in the same topic listed above. If they feel too difficult, start by reviewing the equation definitions in the box at the top of this page and then return to question 1.