# Homework Help: Car drive S units in T time ,prove that there is a point where acceleration > 4S/T^2

1. Dec 22, 2009

### no_alone

1. The problem statement, all variables and given/known data
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 $$\frac{4S}{T^{2}}$$

the car start the drive from speed 0 and end the drive in speed 0
I know this is physic related question but I have in in calculus 2

2. Relevant equations
I almost sure you have to solve the question with taylor polynomial

3. 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 $$\frac{4S}{T^{2}}$$

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.

2. Dec 22, 2009

### TheForumLord

Re: car drive S units in T time ,prove that there is a point where acceleration > 4S/

Do it this way:
x(t)= x(0)+v(0)*t + a(c1)*t^2/2 when 0<c1<t...
So we'll get: x(t)=a(c1)/2 * t^2
If t=T/2 -> x(T/2) =a(c1)*T^2 /8....

Around T we'll get:
x(t) = S + a(c2)/2 * (t-T)^2 .... Put T/2 as t... Put both things you've got in equality and you're done :)

3. Dec 22, 2009

### no_alone

Re: car drive S units in T time ,prove that there is a point where acceleration > 4S/

Isn't the internet small
Thank you very much..
This was my very first try, But I thought , Ha c1 isn't c2 each one has a diffrent area and I got confused and stooped going this way.
...
Thanks.

4. Dec 22, 2009

### TheForumLord

Re: car drive S units in T time ,prove that there is a point where acceleration > 4S/

The whole world is a small place to live in :)

Anyway, which other courses you took this semester?