Speed and velocity

AshPhys · Revision cheat sheet

AS Level9702 AS Ch.1Chapter 1: KinematicsLesson 1.3Sections 1.3

Goal: Calculate average velocity from displacement and contrast it with average speed.

01The big picture

Velocity is the rate of change of displacement: speed in a stated direction. It is a vector, so it uses displacement, not distance.

In a straight line, choose one direction as positive; a negative velocity then means moving the other way. Average speed and average velocity differ whenever the motion turns back: a round trip has an average velocity of zero.

Velocity [paraphrase]: The rate of change of displacement (displacement per unit time), with a direction.
Average velocity [paraphrase]: Total displacement divided by total time.

02Key equations

Average velocity (Δs: displacement)

v = \frac{\Delta s}{\Delta t}

Average speed (d: distance)

\text{speed} = \frac{d}{t}

Symbols and units

$v$ velocity $\mathrm{m\,s^{-1}}$
$\Delta s$ change in displacement $\mathrm{m}$
$d$ distance travelled $\mathrm{m}$
$\Delta t,\ t$ time $\mathrm{s}$

03Sample problems with solutions

Sample 1 · There and partly back
A car drives 300 m east in 20 s, then 100 m west in 10 s. Calculate its average speed and its average velocity for the whole trip.

Speed uses the total distance:
$\text{speed} = \frac{300 + 100}{20 + 10} = \frac{400}{30} = 13.3\ \mathrm{m\,s^{-1}}$
Velocity uses the displacement (east positive):
$v = \frac{300 - 100}{30} = \frac{200}{30} = 6.67\ \mathrm{m\,s^{-1}}$

Answer: average speed 13 m s⁻¹; average velocity 6.7 m s⁻¹ east

Unit check:

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

04Practice problems

P1
A ball is thrown 5.0 m straight up and caught at the same height 2.0 s after it was thrown. Calculate its average speed and average velocity.
Final answer
5.0 m s⁻¹; zero
Answer: 5.0 m s⁻¹; zero
P2
A train travels 12 km north in 10 minutes. Calculate its average velocity.
Final answer
20 m s⁻¹ north
Answer: 20 m s⁻¹ north
P3
Can an object have a constant speed but a changing velocity? Explain.
Final answer
Yes, if its direction changes (e.g. moving in a circle).
Answer: Yes, if its direction changes (e.g. moving in a circle).
P4
Taking east as positive, a cyclist has a velocity of −15 m s⁻¹. Describe the motion.
Final answer
15 m s⁻¹ towards the west
Answer: 15 m s⁻¹ towards the west

05Other useful information

Common mistakes

✗ Wrong: Use the total distance to find the average velocity.
✓ Right: Use the displacement (start to finish), with a direction.
✗ Wrong: A negative velocity means slowing down.
✓ Right: It means moving in the negative direction.

Exam tips

State your positive direction before writing any velocity.

What the syllabus asks

9702 topic 2: define and use speed and velocity. Coursebook 1.3.

Explore: Practice questions for this lesson