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]

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