Is the average velocity of an object going down an inclined ramp equal to the instantaneous velocity of the object at the midpoint of the ramp?

Question

So, I need to verify whether or not the average velocity of an object going down an inclined ramp is equal the instantaneous speed of the object in the midpoint, and I need to figure out a simple way to explain it as well.

Answer 1

Velocity increases linearly with time. This means that average velocity occurs at the midpoint in time, which is definitely not the same as the midpoint in space.

Answer 2

Since the motion is at constant acceleration $a$, we have

• $s=at^2/2\implies t=\sqrt{\frac{2s}a}$

and therefore

• $v=at=\sqrt{2sa}$

which is not linear.