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## Homework Statement

Car start to drive from point A to point B in a straight line ,

The distance from A to B is S, the time the car drove is T

Prove that there is a point in the drive where the acceleration of the car does not lower in absolute value from [tex]\frac{4S}{T^{2}}[/tex]

the car start the drive from speed 0 and end the drive in speed 0

I know this is physics related question but I have in in calculus 2

## Homework Equations

I almost sure you have to solve the question with taylor polynomial

## The Attempt at a Solution

When I try built taylor polynomial when f(x) is the speed around x0 = when the speed reach S/T that is the average speed , the speed must reach the average speed

f(X) = f(x0) + f'(c)(x-x0)

f(x) = S/T +f'(c)(x-x0)

Now I do this for x=0 and for x=T and I can get that if the x0 in [0,T/4] or in [3T/4,T] f'(c) that is the acceleration is above [tex]\frac{4S}{T^{2}}[/tex]

When I try to build the polynomial when f(x) is the location and again around x0 = the time the car speed reach S/T, It does not seem to add up, Because I don't really know what value to give to f(x0)...

Thank you for the help.