A-Level — mathsStandard2 min read

Kinematics and SUVAT Equations

Apply the SUVAT equations for constant acceleration at A-Level. Solve problems with displacement, velocity, and time.

Tutor AI Team2026-02-25T01:59:09.131Z

The SUVAT equations describe motion with constant acceleration. They connect displacement ( $s$ ), initial velocity ( $u$ ), final velocity ( $v$ ), acceleration ( $a$ ), and time ( $t$ ).

The SUVAT Equations

$v = u + at$
$s = ut + \frac{1}{2}at^2$
$s = \frac{(u+v)t}{2}$
$v^2 = u^2 + 2as$
$s = vt - \frac{1}{2}at^2$

Strategy

List known quantities ( $s, u, v, a, t$ ).
Identify the unknown.
Choose the equation that uses the three knowns and the unknown.

Worked Example: Example 1

Problem

$u = 5$ m/s, $a = 2$ m/s², $t = 4$ s. Find $s$ .

$s = 5(4) + \frac{1}{2}(2)(16) = 20 + 16 = 36$ m.

Solution

Worked Example: Example 2

Problem

$u = 20$ m/s, $v = 0$ (stops), $a = -4$ m/s². Find $s$ .

$0 = 400 + 2(-4)s$ → $s = 50$ m.

Solution

Worked Example: Vertical Motion

Problem

Ball thrown up at 15 m/s. $g = 9.8$ m/s². Max height: $v = 0$ .

$0 = 225 - 2(9.8)s$ → $s = 11.5$ m.

Solution

Practice Problems

1. $u = 0$ , $a = 3$ , $t = 6$ . Find $v$ and $s$ .
1. A car brakes from 30 m/s to rest in 5 s. Find deceleration and distance.
1. Stone dropped from 80 m. How long to hit the ground?

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Key Takeaways

✓
5 SUVAT equations for constant acceleration.
✓
List knowns → choose the right equation.
✓
Use $g = 9.8$ m/s² for gravity (take positive direction consistently).
✓
These only work for constant acceleration.

Tags:

#a-level#maths#mechanics#kinematics#suvat

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The SUVAT Equations

Strategy

Worked Example: Example 1

Worked Example: Example 2

Worked Example: Vertical Motion

Practice Problems

Key Takeaways

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