The equations of motion

AshPhys · Revision cheat sheet

AS Level9702 AS Ch.2Chapter 2: Accelerated motionLesson 2.8Sections 2.8

Goal: Choose and use the right suvat equation for uniform acceleration in a straight line.

01The big picture

For uniform (constant) acceleration in a straight line, five quantities describe the motion: $s$ , $u$ , $v$ , $a$ and $t$ . Each equation links four of them, so if you know three you can find the others.

Pick the equation that leaves out the quantity you neither know nor need. Choose a positive direction and give every vector ( $s$ , $u$ , $v$ , $a$ ) a sign.

suvat equations [paraphrase]: The four equations of uniformly accelerated motion in a straight line.

02Key equations

No s

v = u + at

No a

s = \tfrac{1}{2}(u + v)\,t

No v

s = ut + \tfrac{1}{2}at^{2}

No t

v^{2} = u^{2} + 2as

Symbols and units

$s$ displacement $\mathrm{m}$
$u,\ v$ initial, final velocity $\mathrm{m\,s^{-1}}$
$a$ acceleration (constant) $\mathrm{m\,s^{-2}}$

03Sample problems with solutions

Sample 1 · Braking distance
A car travelling at 25 m s⁻¹ brakes with a constant deceleration of 5.0 m s⁻². Calculate its stopping distance.

Known: $u = 25$ , $v = 0$ , $a = -5.0$ . Unknown: $s$ . No $t$ , so use $v^2 = u^2 + 2as$ :
$0 = 25^{2} + 2(-5.0)\,s$
Rearrange for $s$ :
$s = \frac{625}{10} = 62.5\ \mathrm{m}$

Answer:

s = 63\ \mathrm{m}

(2 s.f.)

Unit check:

\frac{(\mathrm{m\,s^{-1}})^{2}}{\mathrm{m\,s^{-2}}} = \mathrm{m}\ \checkmark

04Practice problems

P1
A car accelerates from rest at 2.0 m s⁻² for 8.0 s. How far does it travel?
Final answer
64 m
Answer: 64 m
P2
A train speeds up from 10 m s⁻¹ to 30 m s⁻¹ over 400 m. Find its acceleration.
Final answer
1.0 m s⁻²
Answer: 1.0 m s⁻²
P3
A ball is thrown straight up at 15 m s⁻¹. Find its maximum height ( $g = 9.81$ m s⁻²).
Final answer
11.5 m (11 m)
Answer: 11.5 m (11 m)
P4
A cyclist at 4.0 m s⁻¹ accelerates at 1.5 m s⁻² for 6.0 s. Find the final velocity.
Final answer
13 m s⁻¹
Answer: 13 m s⁻¹

05Other useful information

Common mistakes

✗ Wrong: Make $a$ positive when the object slows down.
✓ Right: If $u$ is positive and it slows, $a$ is negative.

Exam tips

Write “s = ?, u = …, v = …, a = …, t = …” first; the empty slot picks the equation.

What the syllabus asks

9702 topic 2: solve problems with the suvat equations. Coursebook 2.8.

Explore: Practice questions for this lesson