Which of the following graphs are straight lines ? A. Distance – time graph of…

On a motion graph, the shape of the curve depends on how the plotted quantity varies with time. If a quantity stays constant, its graph against time is a horizontal straight line. If a quantity varies linearly with time (a first-degree relation), the graph is an inclined straight line. If a quantity varies as a quadratic function of time (it has a t2 term), the graph is a curve, a parabola, not a straight line.

1. A. Distance-time graph of a body at rest: distance does not change with time, so distance stays constant. This plots as a horizontal straight line.

2. B. Velocity-time graph of a body moving with uniform acceleration: velocity follows v = u + at, a first-degree equation in time with slope a. This plots as an inclined straight line.

3. C. Distance-time graph of a body moving with uniform acceleration: distance (displacement along the path, assuming the motion does not reverse direction) follows s = ut + 1/2 at2, a quadratic equation in time. This plots as a curve, a parabola, not a straight line.

4. D. Velocity-time graph of a body at rest: velocity stays at zero throughout, so velocity is constant at zero. This plots as a horizontal straight line.

This matches the link between the two graphs: velocity is the rate of change of distance. Where velocity is constant (A and D), distance either stays fixed or changes at a constant rate, both straight-line relationships; where velocity itself changes linearly with time (B), the underlying displacement relation gains a t2 term (C, assuming the motion does not reverse direction), which is exactly why the distance-time graph curves while the velocity-time graph stays straight.

So the straight-line graphs are A, B and D.