Question

An automobile traveling at $120km/hr$ was applied brakes and skids to stop in order to avoid hitting a deer. If the automobile had been traveling at $60km/hr$, how much faster would it has to be stopped?

• A. $4$ times the distance
• B. $2$ times the distance
• C. $1/2$ the distance
• D. $1/4$ the distance
• E. Not enough information to tell

Answer 1

The correct option is D $1/4$ the distance

Given : $u=120km/hr$ $v=0$ $km/hr$

Let the distance between the deer and the autotmobile be $x$.

Using $v^2-u^2=2aS$

$\therefore$ $0-(120{)}^2=2ax$ $⟹a=-\frac{60\times 120}{x}$

Now the initial velocity of the automobile $u=60km/hr$

Using $v^2-u^2=2aS$

$\therefore$ $0-(60{)}^2=2\times \frac{-60\times 120}{x}\times x_1$ $⟹$ $x_1=\frac{x}{4}$

Hence the automobile has to apply brakes at $\frac{1}{4}th$ of the initial distance.