Question

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

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

Hint:

If displacement is proportional to the cube of time, the acceleration increases with time as well.

Answer 1

The Correct Option is A

Step 1: Express displacement.
Let the displacement \( x \) be proportional to the cube of time: \[ x = k t^3 \] where \( k \) is a constant.
Step 2: Find velocity and acceleration.
Velocity is the first derivative of displacement with respect to time: \[ v = \frac{dx}{dt} = 3kt^2 \] Acceleration is the derivative of velocity with respect to time: \[ a = \frac{dv}{dt} = 6kt \] Since acceleration is directly proportional to time, it increases with time.