Integrating to find velocity and position equations

[uchicago2012]

Homework Statement

The acceleration of a certain particle is a function of time: a(t) = pt²-qt³, where p and q are constants. Initially, the velocity and position of the particle are zero.
(a) What is the velocity as a function of time?
(b) What is the position as a function of time?

The Attempt at a Solution

I was just wondering if these looked correct:
a) I integrated a(t) to get
v(t) = p(t³/3) - q(t⁴/4) + c
then subbed in v(0) = 0 to find c = 0
so v(t) = p(t³/3) - q(t⁴/4)

b) Then I integrated v(t) to get
x(t) = p(t⁴/12) - q(t⁵/20) + c
then subbed in x(0) = 0 to find c =0
so x(t) = p(t⁴/12) - q(t⁵/20)

 

[danielatha4]

looks good to me