SUVAT equations

The idea

With constant acceleration, five equations link $s$ , $u$ , $v$ , $a$ and $t$ : $v = u + at$ , $s = ut + \frac{1}{2}at^2$ , $s = \frac{1}{2}(u + v)t$ , $v^2 = u^2 + 2as$ and $s = vt - \frac{1}{2}at^2$ .

List $s, u, v, a, t$ and fill in the three you know.
Choose the equation without the quantity you neither know nor want.
Keep one positive direction; for vertical motion $a = -9.8$ if up is positive.

Watch out SUVAT only works when the acceleration is constant.

See it worked

Worked example

A particle has $u = 3\text{ m s}^{-1}$ and $a = 2\text{ m s}^{-2}$ . Find $v$ and $s$ after $5\text{ s}$ .

$v = u + at = 3 + 2 \times 5 = 13\text{ m s}^{-1}$ .
$s = ut + \frac{1}{2}at^2 = 15 + 25$ .
$s = 40\text{ m}$ .

Answer $v = 13\text{ m s}^{-1}$ , $s = 40\text{ m}$

Your turn

Question 1Non-calculator3 marks

A car travelling at $25\text{ m s}^{-1}$ brakes with constant deceleration $5\text{ m s}^{-2}$ . Find its stopping distance.

Question 2Non-calculator3 marks

A ball is thrown vertically upwards at $14.7\text{ m s}^{-1}$ . Find the time it takes to reach its highest point. Use $g = 9.8\text{ m s}^{-2}$ .

Question 3Calculator allowed3 marks

A stone is dropped from rest and falls for $3\text{ s}$ . How far does it fall? Use $g = 9.8\text{ m s}^{-2}$ .

In past papers

40 official questions in 26 papers since 2018. The latest:

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