Finding initial position

[kggirl]

Can someone please help with this problem: The acceleration of a body is given by a[t] = 10cos[pi t]. Its initial position and velocity are given by v[0] =0 and s[0] =0.
a. Find the position at time t.
b. Find the position when t = 1/3

Here is what I have so far:

a[t] = 10cos[pi t] v[0] =0 and s[0] =0.
a[t] = 10cos[pi t] = dV/dt
V[t] = 10* pi sin[pi t] + C = pi sin[pi t] + C
V[0] = pi sin[0] +C , C must = 0
V[t] = pi sin[pi t] = dS/dt
S[t] = pi cos[pi t] + C2 = [cos pi t] + C2
S[0] = cos[0] + C2 = 0 , C2 = -1

a. S[t] = cos(pi(-1)) = -cos pi
b. when t = 1/3, s[1/3] = cos[pi *1/3] = 1.0471975512

Can someone please help with this?

 

[Gene]

d(sin(u)) = cos(u)du
u=pi*t
d(sin(pi*t)) =
cos(pi*t)d(pi*t) =
pi*cos(pi*t)dt so
integral cos(pi*t)dt = (1/pi)sin(pi*t)
Compare that to your V(t)