Question

Why is the total velocity of a roller coaster zero at the end of the ride? How does it’s speed vary with its location?

Answer 1

Total velocity is also known as average velocity

It is given by the formula

`\vec v = (displacement)/(time)`

so here as roller coaster comes to the end of its trip its initial and final position will be same

SO we can say in such type of motions where initial and final position is same then the displacement will always be zero

so average velocity or total velocity will be

`\vec v = (0)/(t) = 0`

so at the end of the trip the net velocity will always be zero

Now if we come at the speed at different point of the motion then we can see that at different points the speed will always be different as here it is the instantaneous speed

this speed is given as

`v = (dx)/(dt)`

now as the roller coaster is moving up then this instantaneous speed will decrease and as it move down then this speed will increase and so on

So at different points the speed may be different