a particle is moving as given by the data below

Question

v(t)= 5sin(t)-2cos(t) ; s(0)= 0

Answer 1

Step 1:

A particle is moving with a velocity

Basic formula for velocity , where is distance.

If is an anti derivative of the function , then the most anti derivative of the function is

.

Where is an arbitrary constant.

Since the anti derivative of  is and the anti derivative of is .

Step 2:

Here .

Substitute in

Substitute value in

Solution:

The position of the particle is