Calculating acceleration

AshPhys · Revision cheat sheet

AS Level9702 AS Ch.2Chapter 2: Accelerated motionLesson 2.2Sections 2.2

Goal: Use a = (v − u)/t and rearrange it for v, u or t.

01The big picture

For an object with initial velocity $u$ that reaches final velocity $v$ after a time $t$ , the acceleration is the change in velocity divided by the time.

The same equation, rearranged, gives the final velocity: $v = u + at$ . To find the time, $t$ is in the denominator, so swap it with the lone term $a$ in one step (cross-multiplication): $t = (v - u)/a$ .

Initial velocity $u$ [paraphrase]: The velocity at the start of the time interval.
Final velocity $v$ [paraphrase]: The velocity at the end of the time interval.

02Key equations

Acceleration

a = \frac{v - u}{t}

Final velocity

v = u + at

Time (swap t and a)

t = \frac{v - u}{a}

Symbols and units

$u$ initial velocity $\mathrm{m\,s^{-1}}$
$v$ final velocity $\mathrm{m\,s^{-1}}$
$t$ time taken $\mathrm{s}$

03Sample problems with solutions

Sample 1 · Velocity and time
A car moving at 5.0 m s⁻¹ accelerates uniformly at 2.0 m s⁻². Calculate (a) its velocity after 6.0 s and (b) the time it takes to reach 25 m s⁻¹.

(a) Final velocity:
$v = u + at = 5.0 + 2.0 \times 6.0 = 17\ \mathrm{m\,s^{-1}}$
(b) $t$ is in the denominator: swap $t$ and $a$ .
$t = \frac{v - u}{a} = \frac{25 - 5.0}{2.0} = 10\ \mathrm{s}$

Answer: (a) 17 m s⁻¹ (b) 10 s

Unit check:

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

04Practice problems

P1
A train slows from 20 m s⁻¹ to 8.0 m s⁻¹ in 6.0 s. Calculate its acceleration.
Final answer
−2.0 m s⁻²
Answer: −2.0 m s⁻²
P2
A stone falls from rest with $a = 9.81$ m s⁻². Find its velocity after 1.5 s.
Final answer
14.7 m s⁻¹ (15 m s⁻¹)
Answer: 14.7 m s⁻¹ (15 m s⁻¹)
P3
A plane needs 75 m s⁻¹ to take off and accelerates from rest at 2.5 m s⁻². How long does it take?
Final answer
30 s
Answer: 30 s
P4
A cyclist at 6.0 m s⁻¹ decelerates at 0.80 m s⁻². How long until they stop?
Final answer
7.5 s
Answer: 7.5 s

05Other useful information

Common mistakes

✗ Wrong: Use $v - u$ the wrong way round.
✓ Right: Always final minus initial; a negative answer means slowing down.
✗ Wrong: Use $a = +0.80$ m s⁻² for a deceleration.
✓ Right: Use $a = -0.80$ m s⁻², or the time comes out negative.

Exam tips

List $u$ , $v$ , $a$ , $t$ with units before you substitute.

What the syllabus asks

9702 topic 2: define and use acceleration. Coursebook 2.2.

Explore: Practice questions for this lesson