Physics- velocity/ distance problem?

[J.live]

Homework Statement

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?

Homework Equations

v=at

The Attempt at a Solution

I integrated the equation its not coming out right

what am i doing wrong?

If someone can kindly explain.

Here is the attachment

 

[zorro]

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

 

[J.live]

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

 

[zorro]

you have to integrate the equation not differentiate

 

[J.live]

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

Do i substitute the answer in equation v=at? Or i can't use that equation at all since a is time dependent.

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

 

[zorro]

We derive the equation v=u+at assuming that acceleration is constant.
here acceleration is time dependent
dv/dt = a
dv=adt
substitute a with the equation you have
integrate both sides of the equation with limits 0 to v and 0 to t respectively
after this you get an equation of v as a funtion of time.
substitute t=7.5s in this equation to get velocity at that time.