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Q. 50

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Found in: Page 62

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# Two cars are driving at the same constant speed on astraight road, with car 1 in front of car 2. Car 1 suddenly startsto brake with constant acceleration and stops in 10 m. At theinstant car 1 comes to a stop, car 2 begins to brake with thesame acceleration. It comes to a halt just as it reaches the back of car 1. What was the separation between the cars before they starting braking?

The separation between the two cars before they starting braking is $20m.$

See the step by step solution

## Step 1: Introduction

If we consider that the car 1 is 'd' distance ahead of the car 2.

Distance travelled by the car 1 before stop is equal to $s=10m.$

## Step 2: Calculation of initial speed

Final velocity of car 1 is, $v=0$

Both the cars have an initial speed of $u.$

We can find the initial speed of the car 1 as, localid="1648229426605" $0={u}^{2}-2as$

Therefore,

localid="1649233598509" role="math" ${u}^{2}=2as\phantom{\rule{0ex}{0ex}}{u}^{2}=2a×10m\phantom{\rule{0ex}{0ex}}{u}^{2}=\left(20\text{m}\right)a...\left(i\right)$

## Step 3: Calculation of distance

Now, the distance travelled by the car 2 in time $t,$

localid="1648230229587" $d=ut\phantom{\rule{0ex}{0ex}}d=u×\frac{u}{a}\left(ast=\frac{u}{a}\right)\phantom{\rule{0ex}{0ex}}d=\frac{{u}^{2}}{a}...\left(ii\right)$

Combining $\left(i\right)and\left(ii\right)$,

localid="1648230309339" $d=\frac{\left(20\text{m}\right)a}{a}\phantom{\rule{0ex}{0ex}}d=20\text{m}$

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