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.

Assuming it's accelerating due to gravity then I wouldn't expect it to be. Such a point exists by the mean value theorem but it's unlikely to be the midpoint. — CyclotomicField, Sep 05 '18 at 00:25
@IsaacLee Please recall that if the OP is solved you can evaluate to accept an answer among the given, more details HERE — user, Oct 23 '18 at 21:02

score 4 · Answer 1 · answered Sep 05 '18 at 00:38

4

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.

answered Sep 05 '18 at 00:38

TonyK

64,559

So if an object going down a 2.4-meter ramp takes 2.85 seconds, if we find the average speed it would be 0.84m/s, so at 1.425 seconds, the instantaneous velocity of the object will be the same as the average speed 0.84m/s? – Isaac Lee Sep 05 '18 at 03:48
@Isaac: That is correct. – TonyK Sep 05 '18 at 10:15

score 1 · Answer 2 · answered Sep 05 '18 at 00:50

1

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.

answered Sep 05 '18 at 00:50

user

154,566

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?

2 Answers2