The displacement of a body is proportional to the cube of the time lap

1.	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» 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.

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»

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.