Practice Velocity in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

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

Example 2

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

Example 3

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

Example 4

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 5

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 6

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

Example 7

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 8

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 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.

Example 10

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 11

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 12

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 13

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

Example 14

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 15

easy
Convert 54 km/h54 \text{ km/h} to m/s.

Example 16

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 17

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 18

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

Example 19

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.

Example 20

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.
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