Velocity Examples in Physics

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 m150 \text{ m} east in 10 s10 \text{ s}. What is its average velocity?

Answer

vavg=15 m/s eastv_{\text{avg}} = 15 \text{ m/s east}

First step

1
Average velocity is displacement divided by time.

Full solution

  1. 2
    Here the displacement is 150 m150 \text{ m} east and the time is 10 s10 \text{ s}.
  2. 3
    vavg=ΔxΔt=15010=15 m/s eastv_{\text{avg}} = \frac{\Delta x}{\Delta t} = \frac{150}{10} = 15 \text{ 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 m200 \text{ m} north in 40 s40 \text{ s}, then 200 m200 \text{ m} south in 60 s60 \text{ s}. What is the average velocity and average speed?

Example 3

medium
A car accelerates from 10 m/s10 \text{ m/s} to 30 m/s30 \text{ m/s} in 5 seconds5 \text{ seconds}. Find the average velocity.

Example 4

medium
A particle's position is x(t)=5t−2t2x(t) = 5t - 2t^2 (in meters, t in seconds). Find the instantaneous velocity at t=1 st = 1 \text{ s} and the time when the velocity is zero.

Example 5

medium
On a position-time graph, the line from (2 s,6 m)(2\,\text{s}, 6\,\text{m}) to (8 s,24 m)(8\,\text{s}, 24\,\text{m}) is straight. Find the velocity.

Example 6

medium
An object's position is r⃗(t)=(2t)x^+(3t2)y^\vec{r}(t) = (2t)\hat{x} + (3t^2)\hat{y} in meters. Find the velocity vector at t=2 st = 2 \text{ s} and its speed.

Example 7

hard
A particle has position x(t)=4t−t3x(t) = 4t - t^3 (in meters). Find (a) average velocity from t=0t = 0 to t=2 st = 2 \text{ s} and (b) instantaneous velocity at t=1 st = 1 \text{ s}.

Example 8

hard
A cyclist accelerates from 5 m/s5 \text{ m/s} to 11 m/s11 \text{ m/s} at constant acceleration over 30 m30 \text{ m}. Find the time taken.

Example 9

challenge
A particle moves so that x(t)=e−tsin⁡(2t)x(t) = e^{-t}\sin(2t) (in meters, t in seconds). Find the velocity at t=0t = 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)=3t2+2tx(t) = 3t^2 + 2t. What is the instantaneous velocity at t=4 st = 4 \text{ s}?

Example 2

medium
A car drives 120 km120 \text{ km} north in 1.5 hours1.5 \text{ hours}, then 80 km80 \text{ km} south in 1 hour1 \text{ hour}. Find: (a) average speed, (b) average velocity.

Example 3

easy
An object moves 2020 m in 44 s in the positive direction. Find its velocity.

Example 4

easy
A car has displacement −30-30 m in 66 s. Find its velocity.

Example 5

easy
Convert: a velocity of 7272 km/h to m/s.

Example 6

easy
A train travels 150150 m east in 1010 s. State the velocity with direction.

Example 7

easy
An object's velocity is constant at 88 m/s. How far does it go in 55 s?

Example 8

easy
Is 3030 m/s a speed or a velocity?

Example 9

easy
A particle moves from x=10x=10 m to x=2x=2 m in 22 s. Find its velocity.

Example 10

easy
An object at constant velocity covers 1212 m in 33 s, then 1212 m in 33 s. What is its velocity throughout?

Example 11

medium
A cyclist rides 99 km/h for 22 h then 1515 km/h for 11 h, all east. Find the average velocity.

Example 12

medium
A runner goes 100100 m east in 2020 s, then 100100 m west in 2020 s. Find the average velocity.

Example 13

medium
A particle's position is x(t)=5tx(t)=5t m. Find its velocity.

Example 14

medium
A boat moves 66 m/s east relative to water; water flows 22 m/s east. Find the boat's velocity relative to ground.

Example 15

medium
Going upstream, a boat does 66 m/s east relative to water while water flows 22 m/s west. Ground velocity?

Example 16

medium
A car accelerates from 00 to 2020 m/s in 55 s. What is its average velocity assuming constant acceleration?

Example 17

challenge
A car drives 6060 km at 6060 km/h, then 6060 km at 3030 km/h, all east. Find the average velocity.

Example 18

challenge
A plane flies 300300 m/s east; wind blows 4040 m/s north. Find the plane's ground velocity magnitude (round to nearest m/s).

Example 19

challenge
A particle's velocity is +3+3 m/s for 44 s then −3-3 m/s for 44 s. Compare its average velocity and average speed.

Example 20

medium
A particle has displacement +24+24 m in 66 s while moving along a line. Find the average velocity.

Example 21

medium
A plane flies 150150 m/s east; a crosswind adds 00 but a 4040 m/s east tailwind acts. Ground velocity east?

Example 22

medium
A car's velocity is +12+12 m/s; 44 s later it is +12+12 m/s. What is the average velocity over the interval if the displacement was 4848 m?

Example 23

easy
A runner covers 400 m400 \text{ m} around a circular track in 80 s80 \text{ s} and ends up at the same starting point. Find the average velocity.

Example 24

easy
A skateboarder moves with constant velocity 4 m/s4 \text{ m/s} east for 12 s12 \text{ s}. Find the displacement.

Example 25

easy
An ant walks 0.50 m0.50 \text{ m} north in 5.0 s5.0 \text{ s}. Find its average velocity.

Example 26

medium
A car travels 60 km60 \text{ km} at 40 km/h40 \text{ km/h}, then 60 km60 \text{ km} at 60 km/h60 \text{ km/h}, all in the same direction. Find the average speed.

Example 27

medium
A boat heads east at 3.0 m/s3.0 \text{ m/s} relative to water; the river flows south at 4.0 m/s4.0 \text{ m/s}. Find the boat's velocity relative to ground (magnitude and direction).

Example 28

medium
A car traveling at 20 m/s20 \text{ m/s} east meets another car traveling at 30 m/s30 \text{ m/s} west. Find the velocity of the second car relative to the first.

Example 29

medium
A jogger runs at 3.0 m/s3.0 \text{ m/s} for the first 4.0 min4.0 \text{ min} and at 5.0 m/s5.0 \text{ m/s} for the next 2.0 min2.0 \text{ min}, all in the same direction. Find the average velocity over the full 6.0 min6.0 \text{ min}.

Example 30

medium
A particle moves so that its position is x(t)=t3−6t2+9tx(t) = t^3 - 6t^2 + 9t (m). Find all times when the velocity is zero.

Example 31

medium
A bus travels 200 km200 \text{ km} east, then 50 km50 \text{ km} west, taking 5 h5 \text{ h} total. Find (a) average speed and (b) average velocity.

Example 32

hard
A plane flies at 250 km/h250 \text{ km/h} heading due north, but a wind blows it east at 60 km/h60 \text{ km/h}. Find the magnitude and direction of the ground velocity.

Example 33

hard
An object's velocity-time graph rises linearly from 00 at t=0t = 0 to 20 m/s20 \text{ m/s} at t=5 st = 5 \text{ s}, stays at 20 m/s20 \text{ m/s} until t=10 st = 10 \text{ s}, then linearly drops to 00 at t=15 st = 15 \text{ s}. Find the total displacement.

Example 34

hard
A car decelerates uniformly from 25 m/s25 \text{ m/s} to rest over 10 s10 \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 m/s20 \text{ m/s}. Take up as positive and g=10 m/s2g = 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 m/s30 \text{ m/s} and train B moves east at 20 m/s20 \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 r⃗1=(3x^+4y^) m\vec{r}_1 = (3\hat{x} + 4\hat{y}) \text{ m} in 2 s2 \text{ s}, then r⃗2=(5x^−2y^) m\vec{r}_2 = (5\hat{x} - 2\hat{y}) \text{ m} in 3 s3 \text{ s}. Find the average velocity vector over the total 5 s5 \text{ s}.

Example 38

challenge
A car travels half the distance to a destination at 30 m/s30 \text{ m/s} and the other half at 60 m/s60 \text{ m/s}. Find the average speed over the trip.
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Background Knowledge

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

displacement