# If the displacement of a body is proportional to square of time, state whether the body is moving with uniform velocity or uniform acceleration.

Let the displacement of the body be $y$ and the time taken be $t$. Then, according to the question, $y ∝ t^2$ $y = kt^2$ where, $k$ is a proportionality constant. Now,

$\text{Velocity}=\frac{dy}{dt}=2kt$

$\text{Acceleration}=\frac{d^2y}{dt^2}=2k$

Therefore, acceleration of the body is constant. So, the body is moving with uniform acceleration and non uniform velocity.

[Read: Motion in a Straight Line]