Question

Give the shape of the velocity-time graph for uniformly accelerated motion along a straight path.

Answer 1

Uniformly accelerated motion

1. We know that a change in velocity with respect to time is called acceleration.
2. We can write Acceleration $=\frac{\mathrm{Final}\mathrm{velocity}-\mathrm{Initial}\mathrm{velocity}}{\mathrm{Time}}=\frac{\mathrm{dv}}{\mathrm{dt}}$
3. Acceleration is a vector quantity.
4. When a body moves in a straight line and its velocity increases in equal amounts over equal time intervals, the motion is referred to as uniformly accelerated motion.

The shape of the velocity-time graph for the uniformly accelerated motion:

1. The slope of the velocity-time graph gives acceleration.
2. Since the acceleration is uniform along a straight path, Thus the slope of the velocity-time graph and the shape of the velocity-time graph for uniformly accelerated motion are also constant.

Slope: $\tan \theta =\frac{v}{t}=a$, Here a is acceleration.