If the velocity of a particle is varying linearly with the time, then shape of the d-t curve would be:

Explanation

If the velocity of a particle is varying linearly with time, then the shape of the distance-time (d-t) curve would be a quadratic curve. Let's understand why: Linear velocity vs. time relationship: If the velocity is varying linearly with time, it means the velocity is changing at a constant rate. In other words, the particle's speed is increasing or decreasing by a constant amount with each unit of time. Distance vs. time relationship: When velocity varies linearly, the distance traveled by the particle will not change linearly with time. Instead, it will change quadratically with time. When velocity varies linearly, the distance-time relationship becomes quadratic because the distance traveled is related to the area under the velocity-time curve. Since the velocity-time curve is a straight line (linear), the area under it will form a quadratic curve (parabolic) when plotted against time. So, the shape of the d-t curve for a particle with linearly varying velocity will be quadratic.