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 is a vector quantity—it has both magnitude (speed) and a direction.

Common stuck point: Speed is just the magnitude of velocity; velocity also includes direction.

Sense of Study hint: When solving a velocity problem, first identify the displacement (change in position) and the time interval. Then divide displacement by time: v = \Delta x / \Delta t. Finally, include the direction in your answer — velocity is a vector, so '5 m/s north' is a complete answer while '5 m/s' alone is just speed.

Worked Examples

Example 1

easy
A car travels 150 \text{ m} east in 10 \text{ s}. What is its average velocity?

Solution

  1. 1
    Average velocity is displacement divided by time.
  2. 2
    Here the displacement is 150 \text{ m} east and the time is 10 \text{ s}.
  3. 3
    v_{\text{avg}} = \frac{\Delta x}{\Delta t} = \frac{150}{10} = 15 \text{ m/s east}

Answer

v_{\text{avg}} = 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 \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} to 30 \text{ m/s} in 5 \text{ seconds}. Find the average velocity.

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.
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Background Knowledge

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

displacement