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t(seconds) 0 1 2 3 4 5
s(feet) 0 10 32 70 119 178

Find the average velocity for the time period beginning when t=2 and lasting

1.3s

Estimate the instantaneous velocity when t=2

  • math -

    0 0
    1 10
    2 32
    3 70
    4 119
    5 178

    Lets approximate this x versus time curve with a parabola between t = 2 and t = 4
    x = a t^2 + b t + c

    32 = 4 a + 2 b + c
    70 = 9 a + 3 b + c
    119 = 16 a + 4 b + c

    solve for a, b and c
    then find x at t = 3.3
    subtract x at 2 which is 32
    divide by 1.3
    that is an approximation for average speed between t = 2 and t = 3.3

    for speed at t = 2
    dx/dt = 2 a t + b
    or just approximate slope at two by
    (x at 3 - x at 1)/2 seconds
    = (70-10)/2 = 30 ft/s

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