SOLUTION: a long distance runner has an average speed of 5 m/s during a race. how far does the runner travel in 25 minutes? express the answer in m, km, and miles. and lastly, A rock

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Question 485107: a long distance runner has an average speed of 5 m/s during a race. how far does the runner travel in 25 minutes? express the answer in m, km, and miles.
and lastly,
A rock is dropped off the side of a bridge and hits the water below at 2.5 s later. what is the rocks velocity when it hits the water, the average velocity as it fell and the height of the bridge above the water.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Your second problem:

You need to choose the measurement system you want to use. Acceleration due to gravity in kms is , whereas in fps it is . The values are negative because of the convention that up is positive.

I'm just going to do the problem using and then you can substitute the appropriate acceleration value and do the arithmetic.

The instantaneous velocity of a falling body is the integral of acceleration with respect to time plus a constant which is the initial velocity,

Since the rock was dropped we can presume that

Which is to say

Substitute 2.5 seconds for the time because that is what is given and multiply by the appropriate value of . If you use your answer will be in meters per second, but if you use then your answer will be in feet per second.

The height is determined by integrating velocity as a function of time. Very conveniently the function we just evaluated to find the final velocity.

Where the constant of integration is the initial height,

For simplicity's sake, we will take the initial height to be zero and then consider the surface of the water to be some negative height.

Again, we substitute 0 for the initial values and get:

And again, substitute 2.5 for and your chosen value for

John

My calculator said it, I believe it, that settles it