Physics- velocity/ distance problem?

1. Sep 13, 2010

J.live

1. The problem statement, all variables and given/known data

An object starts from rest and has an acceleration given by
a = Bt^2 − 1/2Ct, where B = 4.5 m/s^4 and C = −2.2 m/s^3

(1) What is the object's velocity after 7.5 s? (Indicate the direction with the sign of your answer.)

(2) How far has the object moved after t = 7.5 s?

2. Relevant equations

v=at

3. The attempt at a solution

I integrated the equation its not coming out right

what am i doing wrong?

If someone can kindly explain.

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Last edited: Sep 13, 2010
2. Sep 13, 2010

zorro

Hint
v=at is valid if acceleration is not time dependent (i.e. it is constant)

3. Sep 13, 2010

J.live

So, I am using the wrong equation? What equation should i use?

4. Sep 13, 2010

zorro

you have to integrate the equation not differentiate

5. Sep 13, 2010

J.live

So i have to integrate a= Bt^2- 1/2Ct?

Do i substitute the answer in equation v=at? Or i cant use that equation at all since a is time dependent.

Can you show some work so I have a better idea?

Last edited: Sep 13, 2010
6. Sep 13, 2010

zorro

We derive the equation v=u+at assuming that acceleration is constant.
here acceleration is time dependent
dv/dt = a