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

User Dileepa
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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

User Gary Walker
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