Question

The displacement of a body is proportional to the cube of the time lapsed. The magnitude of the acceleration is:

A. increasing with time 

B. decreasing with time 

C. constant 

D. zero

Answer 1

We know that, 

 \(Displacement\propto\,time^3\) …….1 

Now, \(Velocity=\frac{Displacement}{Time}\) …….2 

From equations 1 and 2, we get, 

\(Velocity\propto\,time^2\) …….3 

Now, we also know that, \(Acceleration =\frac{Change\,in\,velocity}{Time}\) …….4 

From equations 3 and 4, we get,

  \(Acceleration\propto\,time\) 

Since, acceleration is directly proportional with time, so it increases with time. 

Hence option A is correct.