State whether the following statements are true or false:
$(a)$ If the motion is not along a straight line,then path length = magnitude of displacement.
$(b)$ Stopping distance is directly proportional to the initial velocity.
$(c)$ The average speed of an object moving with different speeds is the average of those speeds.
$(d)$ The area under the position-time graph represents the displacement of the moving object.

(NONE) False. For non-linear motion,path length is always greater than the magnitude of displacement.
$(b)$ False. Stopping distance $d_s = \frac{v^2}{2a}$,so it is proportional to the square of the initial velocity.
$(c)$ False. Average speed is defined as the total distance traveled divided by the total time taken,not the arithmetic mean of individual speeds.
$(d)$ False. The slope of the position-time graph represents velocity. The area under a velocity-time graph represents displacement.