Velocity Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Velocity.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The rate of change of position with respect to time, including both magnitude and direction.

How fast something is moving AND which way it's heading—direction is essential.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Velocity starts by naming what changes, over what time interval, and whether direction matters.

Common stuck point: Students often know a formula related to velocity but skip the recognition step: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?

Worked Examples

Example 1

easy

A car travels

150 \text{ m}

east in

10 \text{ s}

. What is its average velocity?

Answer

v_{avg} = 15 m/s east

First step

Average velocity is displacement divided by time.

Full solution

2
Here the displacement is $150 \text{ m}$ east and the time is $10 \text{ s}$ .
3
$v_{avg} = \frac{Δ x}{Δ t} = \frac{150}{10} = 15 m/s east$

Velocity is a vector quantity that includes both speed and direction. Average velocity equals the total displacement divided by the total time.

Example 2

medium

A cyclist rides

200 \text{ m}

north in

40 \text{ s}

, then

200 \text{ m}

south in

60 \text{ s}

. What is the average velocity and average speed?

Example 3

medium

A car accelerates from

10 \text{ m/s}

30 \text{ m/s}

5 \text{ seconds}

. Find the average velocity.

Example 4

medium

A particle's position is

x(t) = 5t - 2t^2

(in meters, t in seconds). Find the instantaneous velocity at

t = 1 \text{ s}

and the time when the velocity is zero.

Example 5

medium

On a position-time graph, the line from

(2\,\text{s}, 6\,\text{m})

(8\,\text{s}, 24\,\text{m})

is straight. Find the velocity.

Example 6

medium

An object's position is

\vec{r}(t) = (2t)\hat{x} + (3t^2)\hat{y}

in meters. Find the velocity vector at

t = 2 \text{ s}

and its speed.

Example 7

hard

A particle has position

x(t) = 4t - t^3

(in meters). Find (a) average velocity from

t = 0

t = 2 \text{ s}

and (b) instantaneous velocity at

t = 1 \text{ s}

Example 8

hard

A cyclist accelerates from

5 \text{ m/s}

11 \text{ m/s}

at constant acceleration over

30 \text{ m}

. Find the time taken.

Example 9

challenge

A particle moves so that

x(t) = e^{-t}\sin(2t)

(in meters, t in seconds). Find the velocity at

t = 0

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

A particle's position is given by

x(t) = 3t^2 + 2t

. What is the instantaneous velocity at

t = 4 \text{ s}

Example 2

medium

A car drives

120 \text{ km}

north in

1.5 \text{ hours}

, then

80 \text{ km}

south in

1 \text{ hour}

. Find: (a) average speed, (b) average velocity.

Example 3

easy

An object moves

20

m in

4

s in the positive direction. Find its velocity.

Example 4

easy

A car has displacement

-30

m in

6

s. Find its velocity.

Example 5

easy

Convert: a velocity of

72

km/h to m/s.

Example 6

easy

A train travels

150

m east in

10

s. State the velocity with direction.

Example 7

easy

An object's velocity is constant at

8

m/s. How far does it go in

5

Example 8

easy

30

m/s a speed or a velocity?

Example 9

easy

A particle moves from

x=10

m to

x=2

m in

2

s. Find its velocity.

Example 10

easy

An object at constant velocity covers

12

m in

3

s, then

12

m in

3

s. What is its velocity throughout?

Example 11

medium

A cyclist rides

9

km/h for

2

h then

15

km/h for

1

h, all east. Find the average velocity.

Example 12

medium

A runner goes

100

m east in

20

s, then

100

m west in

20

s. Find the average velocity.

Example 13

medium

A particle's position is

x(t)=5t

m. Find its velocity.

Example 14

medium

A boat moves

6

m/s east relative to water; water flows

2

m/s east. Find the boat's velocity relative to ground.

Example 15

medium

Going upstream, a boat does

6

m/s east relative to water while water flows

2

m/s west. Ground velocity?

Example 16

medium

A car accelerates from

0

20

m/s in

5

s. What is its average velocity assuming constant acceleration?

Example 17

challenge

A car drives

60

km at

60

km/h, then

60

km at

30

km/h, all east. Find the average velocity.

Example 18

challenge

A plane flies

300

m/s east; wind blows

40

m/s north. Find the plane's ground velocity magnitude (round to nearest m/s).

Example 19

challenge

A particle's velocity is

+3

m/s for

4

s then

-3

m/s for

4

s. Compare its average velocity and average speed.

Example 20

medium

A particle has displacement

+24

m in

6

s while moving along a line. Find the average velocity.

Example 21

medium

A plane flies

150

m/s east; a crosswind adds

0

but a

40

m/s east tailwind acts. Ground velocity east?

Example 22

medium

A car's velocity is

+12

m/s;

4

s later it is

+12

m/s. What is the average velocity over the interval if the displacement was

48

Example 23

easy

A runner covers

400 \text{ m}

around a circular track in

80 \text{ s}

and ends up at the same starting point. Find the average velocity.

Example 24

easy

A skateboarder moves with constant velocity

4 \text{ m/s}

east for

12 \text{ s}

. Find the displacement.

Example 25

easy

An ant walks

0.50 \text{ m}

north in

5.0 \text{ s}

. Find its average velocity.

Example 26

medium

A car travels

60 \text{ km}

40 \text{ km/h}

, then

60 \text{ km}

60 \text{ km/h}

, all in the same direction. Find the average speed.

Example 27

medium

A boat heads east at

3.0 \text{ m/s}

relative to water; the river flows south at

4.0 \text{ m/s}

. Find the boat's velocity relative to ground (magnitude and direction).

Example 28

medium

A car traveling at

20 \text{ m/s}

east meets another car traveling at

30 \text{ m/s}

west. Find the velocity of the second car relative to the first.

Example 29

medium

A jogger runs at

3.0 \text{ m/s}

for the first

4.0 \text{ min}

and at

5.0 \text{ m/s}

for the next

2.0 \text{ min}

, all in the same direction. Find the average velocity over the full

6.0 \text{ min}

Example 30

medium

A particle moves so that its position is

x(t) = t^3 - 6t^2 + 9t

(m). Find all times when the velocity is zero.

Example 31

medium

A bus travels

200 \text{ km}

east, then

50 \text{ km}

west, taking

5 \text{ h}

total. Find (a) average speed and (b) average velocity.

Example 32

hard

A plane flies at

250 \text{ km/h}

heading due north, but a wind blows it east at

60 \text{ km/h}

. Find the magnitude and direction of the ground velocity.

Example 33

hard

An object's velocity-time graph rises linearly from

0

t = 0

20 \text{ m/s}

t = 5 \text{ s}

, stays at

20 \text{ m/s}

until

t = 10 \text{ s}

, then linearly drops to

0

t = 15 \text{ s}

. Find the total displacement.

Example 34

hard

A car decelerates uniformly from

25 \text{ m/s}

to rest over

10 \text{ s}

. Find (a) the average velocity, and (b) the distance traveled.

Example 35

hard

A ball is thrown straight up with initial velocity

20 \text{ m/s}

. Take up as positive and

g = 10 \text{ m/s}^2

. Find the average velocity during the rise (until it reaches maximum height).

Example 36

hard

Train A moves east at

30 \text{ m/s}

and train B moves east at

20 \text{ m/s}

on parallel tracks. Find (a) velocity of A relative to B, and (b) velocity of B relative to A.

Example 37

hard

A drone flies

\vec{r}_1 = (3\hat{x} + 4\hat{y}) \text{ m}

2 \text{ s}

, then

\vec{r}_2 = (5\hat{x} - 2\hat{y}) \text{ m}

3 \text{ s}

. Find the average velocity vector over the total

5 \text{ s}

Example 38

challenge

A car travels half the distance to a destination at

30 \text{ m/s}

and the other half at

60 \text{ m/s}

. Find the average speed over the trip.

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Related Concepts

Displacement Acceleration Speed

Background Knowledge

These ideas may be useful before you work through the harder examples.

displacement