Starting from rest at the top of an inclined plane a body reaches the bottom in 4 seconds. In what time does the body cover one-fourth the distance starting from the top?

The correct option is B

2 s

Let ${}^{\prime }{s}^{\prime }$ be the total distance and ${}^{\prime }{a}^{\prime }$ be the acceleration. As the inclination is constant, a fixed component of gravitation would act along the incline and hence the body would experience a constant acceleration ${}^{\prime }{a}^{\prime }$. Now, we know initial velocity $u=0$

We use the equation of motion
$s=ut+\frac{1}{2}a{t}^2$.................(a)

So, for time $t=4$ seconds,

$s=\frac{1}{2}a\times 4^2$ ....................(1)

To find the time taken for covering $s/4$ distance put it in equation (a)

$\frac{s}{4}=\frac{1}{2}a{t}^2$ ........................ (2)

Now dividing equation (1) by (2)

$\frac{s}{\frac{s}{4}}=\frac{\frac{1}{2}\times a\times 4^2}{\frac{1}{2}\times a\times t^2}$

$t^2=4$

On solving we get time $t=2$ seconds