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A car travels along the curved path with radius of curvature p= 30m such that its speed is increased by at = (0.5e^t) m/s^2, where t is in seconds. determine the magnitudes of its velocity and acceleration after the car has traveled s = 18m starting from rest. neglect the size of the car.

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3 answers

  1. The distance s travelled in time t' is
    S (t') = Double integral a_t dt
    t=0 to t'
    18 = 0.5*e^t' meters
    t' = ln 36 = 3.584 s

    V (t') = Single integral a_t dt
    t=0 to t'
    = 0.5*e^t' = 18 m/s

    a_t (t') = 18 m/s^2

    There is also a centrifugal acceleration component,
    a_r = V(t')^2/R = 324/30 = 10.8 m/s^2

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  2. you're a lifesaver
    thank you!

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  3. Above answer is completely wrong.. it seems he forgot that it's an initial value problem

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