Question

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is

• A. Increasing with time
• B. Decreasing with time
• C. Constant but not zero
• D. Zero

Answer 1

According to the question displacement is proportional to the cube of the time

It can be written as

S = $k{t}^3$

We know that the acceleration is double differentiation of the displacement

$\therefore a=\frac{d^{2}S}{d{t}^2}=6kt$

From the above

$a\propto t$ (increasing with time)

If the acceleration is directly proportional to the time then it will increase with the time.

The correct option is (D) Increasing with time.