Calculus

Find the distance traveled in 45 seconds by an object traveling at a velocity of v(t) = 20 + 2cos(t) feet per second.

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  1. distance expression = 20t + 2sin(t) + c , where c is a constant
    I will assume that you mean the distance in the first 45 seconds.
    position at t=0
    = 0 + 2sin0 + c = c
    position at t = 45
    = 900 + 2sin45 + c

    distance travelled = 90+2sin45 + c - c
    = appr. 901.7 feet

    ( notice in the second 45 seconds, the object would have travelled
    1800 + 2sin90 + c - 900 - 2sin45 - x
    = appr. 900.1 , different from the distance covered in the first 45 seconds.
    If you wanted the actual distance of the path along the sine curve of the object you would have a much more difficult question)

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