Question

A car moving at a speed u is stopped in a certain distance when the brakes produce a deceleration a. If the speed of the car is nu, what must be the deceleration of the car to stop it in the same distance?

• A. $\sqrt{n}a$
• B. $na$
• C. $n^{2}a$
• D. $n^{3}a$

Answer 1

The correct option is C

$n^{2}a$

From the third equation of motion, $v^2=u^2-2as$
$\Rightarrow 0=u^2-2as$
$\Rightarrow s=\frac{u^2}{2a}$
So, the distance over which the car is stopped is given by $s=\frac{u^2}{2a}$.
If initial velocity is $nu$, let the value deceleration to stop the car in the same distance be $a^{\prime }$.
$0^2=(nu{)}^2-2a^{\prime }s\Rightarrow 0=n^2{u}^2-2a^{\prime }\left(\frac{u^2}{2a}\right)\Rightarrow a^{\prime }=n^{2}a$
Hence, the correct choice is (c).