Question

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

Answer 1

Answer: Let displacement be s

So, s is prop to t

3

s=kt

3

 Where k is the proportionality constant

On differentiation

dt

ds

​

=3kt

2

⇒v=3kt

2

On again differentiation

dt

2

d

2

s

​

=6kt

⇒a=6kt

So,a is proportional to t

Where 6k is the proportionality constant

Acceleration is directly proportional to time, it varies linearly with time and increases with respect to time.