Question

How do you solve the following problems? I have to find the position function.

a(t)=t-2, s(0)=1, v(0)=3
a(t)=10sin(t)+3cos(t), s(0)=0, s(2π)=12

Answer 1

a(t)=t-2, s(0)=1, v(0)=3
a(t)=10sin(t)+3cos(t), s(0)=0, s(2π)=12


velocity v= integral of a(t0dt= t^2/2 -2t+3 , where v(0)=3=C1
distance s = integral of v(t)dt= t^3/6 -2t +3t+1, where s(0)=1=C2

can you try it on this one?
a(t)=10sin(t)+3cos(t), s(0)=0, s(2π)=12