Question

Let s(t) denote the position of a particle at time t, and let v and a be the velocity and acceleration respectively. The particle is moving according to the data

a(t)=10sin(t)+3cos(t)
s(0)=-4
s(2pi)=1

find a function describing position of particle

s(t)=???

I do not know where to start, it is unlike other anti-derivative problems I have dealt with. I would prefer an explanation with an answer, thanks.

Answer 1

a(t) is the 2nd derivative of s(t)

v(t) is the 1st derivative of s(t)

take the anti-derivative of a(t)
... this is v(t) + C
... don't forget the unknown constant

take the anti-derivative of v(t)
... this is s(t) + Ct + D
... don't forget the unknown constants

use the two given values for s(t) to find the constants