Question

A particle is moving with the given data. Find the position of the particle.
a(t) = cos t + sin t, s(0) = 1, v(0) = 4

Answer 1

v(0)=-1
s(0)=1

Answer 2

sooo s(t) would be 1?

Answer 3

s(t)=-cost-sint

Answer 4

thank you thank you thank you thank youuuu!!!

Answer 5

sorry s(0)=-1

Answer 6

You have to integrate the function a(t) twice to get it's position function. First we get the velocity function:
v(t)=∫(cost+sint)dt=sint−cost+C
Where C is a constant. Since v(0)=4 we get:
v(0)=sin0−cos0+C=4
-1+C=4
and C=5
Now we integrate the velocity function to get the position function s(t):
s(t)=∫(sint−cost+5)dt=−cost−sint+5t+D
Where D is a constant. We have s(0)=1. So,
s(0)=5(0)−sin(0)−cos(0)+D=1
0-0-1+D=1
D=2
So you position function is:
s(t)=5t-sint-cost+2

Answer 7

Thank you!