Question

Find the distance traveled in 25 seconds by an object traveling at a velocity of v(t) = 20 + 3cos(t) feet per second.

Answer 1

we are given

`v(t)=20+3cos(t)`

For finding distance , we will integrate v(t) from 0 to 25

`distance=\int _0^(25)\left(20+3cos\left(t\right)\right)dt\:`

now, we can solve it

`\int \:20+3\cos \left(t\right)dt`

`=\int \:20dt+\int \:3\cos \left(t\right)dt`

`=20t+3\sin \left(t\right)`

now, we can plug bounds

and we get

`=500+3\sin \left(25\right)-0`

`=3\sin \left(25\right)+500`

`distance=499.60294feet`..............Answer