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A motorist drives along a straight road at a constant speed of 60 m/s. At time t = 0 she passes a parked motorcycle
police o±cer. The o±cer takes o® after her at t = 0 and accelerates according to the formula a(t) = bt, where t is the
time and b is a positive constant. What is the speed of the police o±cer when he reaches the motorist?

  • Physics -

    Well, they travel the same distance in the same time.

    The officers velocity is INT a(t)dt= INT btdt= 1/2 b t^2
    so the officers distance traveled is
    INT 1/2 b t^2 dt= 1/6 b t^3

    set the distances equal

    1/6 b t^3= 60t
    solve for t.

    t^2= 360/b
    t= sqrt(360/b)
    now find the velocity of the officer at that point:
    Vf= 1/2 b t^2= 1/2 b * 360/b=180m/s

    check my work.

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