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Q12.

Expert-verified
Found in: Page 41

### Physics Principles with Applications

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

# You travel from point A to point B in a car moving at a constant speed of $70\mathrm{km}/\mathrm{h}$. Then you travel the same distance from point B to another point C, moving at a constant speed of $90\mathrm{km}/\mathrm{h}$. Is your average speed for the entire trip from A to C, equal to $80\mathrm{km}/\mathrm{h}$? Explain why or why not.

The average speed for the entire trip from point A to C is less than $80\mathrm{km}/\mathrm{h}$.

See the step by step solution

## Step 1. Definition of average speed

Speed is a scalar quantity, which means it has only magnitude. Average speed is the ratio of the total distance traveled by an object to the total time taken to cover the distance.

## Step 2. Comparison between the times taken for traveling from A to B and B to C

Speed at which your car travels from point A to B, ${s}_{1}=70\mathrm{km}/\mathrm{h}$

Speed at which your car covers the same distance from point B to C, ${s}_{2}=90\mathrm{km}/\mathrm{h}$

Thus, you spend more time traveling at $70\mathrm{km}/\mathrm{h}$ than at $90\mathrm{km}/\mathrm{h}$, for the same distance.

## Step 3. Determination of the average speed of the car

Let the distance from point A to B (or point B to C) be y.

Then the total distance travelled will be $2y$.

The time taken (t) by an object to a certain distance is:

$t=\frac{\mathrm{Distance}}{\mathrm{Speed}}$

Time elapsed in traveling from A to B, ${t}_{1}=\frac{y}{70\mathrm{km}/\mathrm{h}}$

Similarly, time elapsed in traveling from A to B, ${t}_{2}=\frac{y}{90\mathrm{km}/\mathrm{h}}$

The average speed is: ${s}_{\mathrm{av}}=\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Total}\mathrm{time}}$

Therefore, the average speed for the entire trip from A to C is:

$\begin{array}{c}=\frac{2y}{\left(\frac{y}{70\mathrm{km}/\mathrm{h}}+\frac{y}{90\mathrm{km}/\mathrm{h}}\right)}\\ =\frac{2×90×70}{90+70}\mathrm{km}/\mathrm{h}\\ =78.75\mathrm{km}/\mathrm{h}\end{array}$

Thus, the average speed for the entire journey is less than $80\mathrm{km}/\mathrm{h}$.