Solving problems with the equations of motion

5 minAS Level2.1.7

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can solve straight-line motion problems with the suvat equations: pick the right equation, keep the signs straight, and handle two-stage journeys.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$s_1$	displacement in the first stage
$s_2$	displacement in the second stage

Same puzzle, different costume

Every suvat question is the same puzzle in a new outfit. There are five quantities. You're given three, you want a fourth, and the fifth you neither know nor care about.

Each equation leaves out exactly one quantity. Pick the one that leaves out the quantity you don't care about.

Equation	Leaves out
$v = u + at$	$s$
$s = \tfrac{1}{2}(u + v)t$	$a$
$s = ut + \tfrac{1}{2}at^2$	$v$
$v^2 = u^2 + 2as$	$t$

The five-step routine

Choose a positive direction and write it down.
List $s, u, v, a, t$ . Fill in what you know (with signs), put ? by what you want.
Pick the equation that leaves out the remaining unknown.
Substitute and solve. Units in SI first: divide $\text{km h}^{-1}$ by 3.6 to get $\text{m s}^{-1}$ .
Sense-check the sign and size.

Decode the hidden values: "from rest" or "dropped" means $u = 0$ ; "comes to rest" or "stops" means $v = 0$ ; "uniformly" or "constant" means you're allowed to use suvat at all.

Worked example: An emergency stop

A car travelling at $25\ \text{m s}^{-1}$ brakes uniformly and stops in $40\ \text{m}$ . Find its acceleration and the time it takes to stop.

Have a go first?

Quick check

Multiple choiceQuestion 1 · Recall

Answer the 2 questions above to continue.