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Q1.

Expert-verified
Found in: Page 67

### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

# One car travels due east at $40\mathrm{km}/\mathrm{h}$, and a second car travels north at $40\mathrm{km}/\mathrm{h}$. Are their velocities equal? Explain.

No, their velocities are not the same because both cars have different directions.

See the step by step solution

## Step 1. Definition of velocity

Velocity is a vector quantity having both magnitude and direction. It is defined as the rate of change of displacement of an object with time.

## Step 2. Identification of the given data

The first car travels eastward at $40\mathrm{km}/\mathrm{h}$. The second car moves along the north direction at $40\mathrm{km}/\mathrm{h}$.

You can write the velocities of the cars as ${\stackrel{\to }{v}}_{1}=\left(40\stackrel{^}{j}\right)\mathrm{km}/\mathrm{h}$ and ${\stackrel{\to }{v}}_{2}=\left(40\stackrel{^}{i}\right)\mathrm{km}/\mathrm{h}$.

## Step 3. Comparison of the velocities

Here, both cars have the same magnitude of velocities, i.e.,$40\mathrm{km}/\mathrm{h}$. However, their directions are not the same; one is moving along the east and the other toward the north. If two vectors have different directions, they are said to be unequal.

Thus, the velocities of these cars are not equal.