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. constant but not zero
• B. increasing with time
• C. zero
• D. decreasing with time

Answer 1

Answer: (B)

increasing with time

Answer 2

Given that displacement of the body,

$y \,\propto\,t^{3}$ or$\,\,\,\,\,y = kt^{3}$

$\therefore\,\,\,\,\,v = \frac{dy}{dt } = 3kt^{2}$ or $\,\,\,\,a = \frac{dv}{dt} = 6\,kt \propto$ t

$\therefore\,\,\,\,\,$ The magnitude of the acceleration of the body increases with time.

Therefore, the correct option is (B): increasing with time