Question

CALCULUS HELP PLEASE (:

Answer 1

sorry to be bothering everyone with these questions, ive just kept these to the side because people havnt been responding on OS and i just dont get how to solve these problems, i appreciate the help(:

Answer 2

@ybarrap please help !

Answer 3

Does this make sense?
$$
a(t)={dv(t)\over dt}\\
\int a(t)dt=\int dv(t)\\
v(t)=\int a(t)dt=\int (2t+\sin t) dt
$$
Can you do this?

Answer 4

yes! im going to do it now, could you check me after?

Answer 5

i got v(t)=t^2+cos(t)+3 @ybarrap

Answer 6

@perl

Answer 7

Check your integration of the sine function.

\[ \int sin(t) dt = -cos(t) + C\]

^_^

Answer 8

Close,
$$
v(t)=\int a(t)dt=\int (2t+\sin t) dt=t^2-\cos t + C
$$
Since you know that \(v(0)=4\) you can find C:
$$
v(0)=4=0^2-\cos 0 + C\\
\implies C=4+1=5
$$
So now you have everything!

Make sense?