SUVAT Equations Worksheet with Answers (PDF): GCSE and A-Level Practice

This page contains a free SUVAT equations worksheet with 10 fully worked questions, 5 at GCSE level and 5 at A-Level, plus a downloadable PDF. Every question includes a step-by-step worked answer. The worksheet covers all 5 SUVAT equations and the most common exam question types.

What Are SUVAT Equations?

SUVAT equations are 5 formulas that describe motion under constant acceleration. The name SUVAT comes from the 5 variables: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). Each equation uses 4 of the 5 variables, which allows a solver to find any unknown when 3 values are known.

What Are the 5 SUVAT Equations?

For exam-board context, AQA’s official 2026 formulae and equation sheet update explains how equation-sheet arrangements apply for GCSE Mathematics, Physics, and Combined Science.

The 5 SUVAT equations are the standard equations of motion used in GCSE Physics, GCSE Maths, and A-Level Mechanics.

Select the equation that contains your 3 known variables and 1 unknown. The variable absent from the problem matches the "Variable Not Included" column.

How Do GCSE and A-Level SUVAT Questions Differ?

GCSE SUVAT questions use 1 equation and 1 unknown. A-Level questions use 2 or more equations, include vertical motion under gravity, or require forming a quadratic.

GCSE SUVAT Practice Questions

The 5 GCSE questions below test each of the 5 SUVAT equations in a direct, 1-step format.

1. A car starts from rest and accelerates at 4 m/s² for 6 seconds. Find the final velocity.
2. A ball rolls with an initial velocity of 8 m/s and decelerates at 2 m/s². Find the displacement after 3 seconds.
3. A cyclist accelerates from 3 m/s to 9 m/s over a distance of 18 m. Find the acceleration.
4. A train travels at 30 m/s and brakes with a deceleration of 5 m/s². Find the stopping distance.
5. A stone is dropped from rest and falls for 4 seconds under gravity (g = 9.8 m/s²). Find the distance fallen.

GCSE SUVAT Worked Answers

Each GCSE answer below states the equation used, substitutes values, and gives the final answer with units.

Question 1 Answer: Final Velocity

Known: u = 0, a = 4 m/s², t = 6 s. Unknown: v. Use v = u + at.

v = 0 + (4)(6) = 24 m/s

Question 2 Answer: Displacement With Deceleration

Known: u = 8 m/s, a = −2 m/s², t = 3 s. Unknown: s. Use s = ut + ½at².

s = (8)(3) + ½(−2)(3²) = 24 − 9 = 15 m

Question 3 Answer: Acceleration From Velocities and Distance

Known: u = 3 m/s, v = 9 m/s, s = 18 m. Unknown: a. Use v² = u² + 2as.

81 = 9 + 2a(18) → 72 = 36a → a = 2 m/s²

Question 4 Answer: Stopping Distance

Known: u = 30 m/s, v = 0, a = −5 m/s². Unknown: s. Use v² = u² + 2as.

0 = 900 + 2(−5)s → 10s = 900 → s = 90 m

Question 5 Answer: Free Fall Distance

Known: u = 0, a = 9.8 m/s², t = 4 s. Unknown: s. Use s = ut + ½at².

s = 0 + ½(9.8)(16) = 78.4 m

A-Level SUVAT Practice Questions

The 5 A-Level questions below require multi-step working, sign conventions, or quadratic equations.

1. A ball is thrown vertically upward at 15 m/s from a point 2 m above the ground. Find the maximum height above the ground. (g = 9.8 m/s²)
2. A particle decelerates uniformly from 20 m/s to rest over 8 seconds. Find (a) the deceleration and (b) the total distance traveled.
3. A stone is projected vertically upward from the top of a 45 m cliff with initial velocity 10 m/s. Find the time for the stone to reach the ground. (g = 9.8 m/s²)
4. A particle moves with initial velocity 5 m/s under constant acceleration. It covers 18 m during the 3rd second of motion. Find the acceleration.
5. Particle A moves from a fixed point at 6 m/s with zero acceleration. Particle B starts from the same point 4 seconds later, with initial velocity 2 m/s and acceleration 2 m/s². Find the time after A starts when B catches A.

A-Level SUVAT Worked Answers

Each A-Level answer states the sign convention, identifies the equation, shows full substitution, and solves completely.

Question 1 Answer: Maximum Height

At maximum height, v = 0. Taking upward as positive: u = 15 m/s, a = −9.8 m/s².

Use v² = u² + 2as → 0 = 225 − 19.6s → s = 225 ÷ 19.6 = 11.48 m above launch point.

Total height above ground = 2 + 11.48 = 13.5 m (3 s.f.)

Question 2 Answer: Deceleration and Distance

(a) Use v = u + at → 0 = 20 + 8a → a = −2.5 m/s²

(b) Use s = ½(u + v)t → s = ½(20 + 0)(8) = 80 m

Question 3 Answer: Time to Reach Ground From Cliff

Take upward as positive. The stone ends 45 m below the launch point, so s = −45 m.

Use s = ut + ½at²: −45 = 10t − 4.9t² → 4.9t² − 10t − 45 = 0.

Quadratic formula: t = (10 ± √(100 + 882)) ÷ 9.8 = (10 ± 31.34) ÷ 9.8.

Taking the positive root: t = 41.34 ÷ 9.8 = 4.22 s (3 s.f.)

Question 4 Answer: Acceleration Using the Nth-Second Formula

Distance in the nth second: s_n = u + a(n − ½). Substitute n = 3, s_3 = 18, u = 5.

18 = 5 + a(2.5) → 13 = 2.5a → a = 5.2 m/s²

Question 5 Answer: When B Catches A

Let t = time in seconds after A departs. B departs at t = 4, so B travels for (t − 4) seconds.

Distance A: s_A = 6t. Distance B: s_B = 2(t − 4) + ½(2)(t − 4)².

Set s_A = s_B: 6t = 2(t − 4) + (t − 4)² → t² − 12t + 8 = 0.

t = (12 ± √(144 − 32)) ÷ 2 = (12 ± 10.58) ÷ 2. Taking the valid root: t = 11.3 s (3 s.f.)

What Are the Most Common SUVAT Mistakes at A-Level?

The 3 most frequent errors are incorrect sign convention, misidentifying displacement as distance, and applying SUVAT when acceleration is not constant.

1. Sign errors: Set a clear positive direction before substituting. Deceleration and gravity (when downward) are negative in the upward-positive convention.
2. Displacement vs distance: A particle returning to its starting point has s = 0, not s = total path length. The 3rd and 4th SUVAT equations use displacement only.
3. Non-constant acceleration: SUVAT does not apply to variable acceleration problems. Those require calculus, specifically integration of the acceleration function.

What Should You Know Before Using This Worksheet?

SUVAT equations apply to straight-line motion under constant acceleration. GCSE questions require 1 equation and 3 known values. A-Level questions add vertical motion under gravity, quadratic equations, and multi-particle scenarios. Assigning a sign convention before every problem eliminates the most common source of error across both levels.