landonaggas landonaggas
  • 23-08-2018
  • Mathematics
contestada

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

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rejkjavik rejkjavik
  • 05-09-2018

we are given

[tex] v(t)=20+3cos(t) [/tex]

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

[tex] distance=\int _0^{25}\left(20+3cos\left(t\right)\right)dt\: [/tex]

now, we can solve it

[tex] \int \:20+3\cos \left(t\right)dt [/tex]

[tex] =\int \:20dt+\int \:3\cos \left(t\right)dt [/tex]

[tex] =20t+3\sin \left(t\right) [/tex]

now, we can plug bounds

and we get

[tex] =500+3\sin \left(25\right)-0 [/tex]

[tex] =3\sin \left(25\right)+500 [/tex]

[tex] distance=499.60294feet [/tex]..............Answer

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Please I need the answer to this ASAP this question is worth 25 points