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Q. 50

Expert-verifiedFound in: Page 62

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

Two cars are driving at the same constant speed on a

straight road, with car 1 in front of car 2. Car 1 suddenly starts

to brake with constant acceleration and stops in 10 m. At the

instant car 1 comes to a stop, car 2 begins to brake with the

same 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 $20m.$

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 $s=10m.$

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

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

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

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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