Question

If the displacement of an object is proportional to the square of time, then the object moves with

• A. Uniform velocity
• B. Uniform acceleration
• C. increasing acceleration
• D. Decreasing acceleration.

Answer 1

The correct option is B

Uniform acceleration

Displacement:

Displacement is defined as the shortest distance between the initial point and the final point.

If the displacement of the object is directly proportional to the square of time, then

$S\propto t^2$

The velocity of the object is,

$$\begin{gathered} v\propto \frac{d}{dt}\left(t^2\right) \\ v\propto 2t \end{gathered}$$

Thus, the acceleration of the object is,

$$\begin{gathered} a\propto \frac{d}{dt}\left(2t\right) \\ a\propto 2 \end{gathered}$$

Thus, the acceleration is constant.

Hence, option (b) is correct.