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

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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

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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.