Question

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

• A. 1 second
• B. 2 second
• C. 3 second
• D. 4 second

Answer 1

The correct option is B

2 second

Step 1: Given data

Let ‘$s$’ be the total distance and ′$a$′ 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 ′$a$′.

Now, we know the initial velocity $u=0.$

Step 2: Using the equation of motion.
The equation of motion is
$s=u\times t+\frac{1}{2}\times a\times t^2$ .................(a)
So, for time $t=4seconds$,
$s=\frac{1}{2}\times a\times 4^2$ ....................(1)
To find the time taken to cover $\frac{s}{4}$ distance put it in equation (a)
$\frac{s}{4}=\frac{1}{2}\times a\times t^2$....................... (2)

Step 3: Now dividing equation (1) by (2)
$\frac{s}{{\displaystyle \raisebox{1ex}{$s$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}=(\frac{1}{2}\times a\times 4^2)/(\frac{1}{2}\times a\times t^2)$
$t^2=4$
On solving we get time
$t=2seconds.$

Hence, option B is correct. 2 seconds.