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If a rock is thrown upward on the planet Mercury with a velocity of 11 m/s, its height in meters t seconds later is given by y = 11t - 1.86t sqaure
a : Find the average velocity over the given time intervals: [1, 2] , [1, 1.5] , [1, 1.1] , [1, 1.01] [1, 1.001]

b: Estimate the instantaneous velocity when t = 1.

  • math -

    The height has been given in terms of t (in seconds) as:
    height=y(t)=11t-1.86t²
    To evaluate the average velocity in a given time interval [t1,t2], you would calculate:
    (y(t2)-y(t1))/(t2-t1)
    where y(t2)=height at t=t2, and
    y(t1)=height at t=t1.
    For example, for the interval
    [0,2],
    height at t=0: y(0)=11(0)-1.18(0)²=0
    height at t=2: y(2)=11(2)-1.18(2)²=17.28
    Average velocity = (y(2)-y(0))/(2-0)=8.64 m s-1

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