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March 25, 2017

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A particle moves at varying velocity along a line and s= f(t) represents the particle's distance from a point as a function of time, t. sketch a graph for f if the average velocity of the particle between t=2 and t=6 is the same as the instantaneous velocity at t=5.

I know that instantaneous velocity is calculated as s(a+h)-s(a)/h but i don't understand what to put in for h. I'm stuck at this point and would appreciate any guidance on what to do next. thanks so much!!!

  • Calc I - ,

    " I know that instantaneous velocity is calculated as s(a+h)-s(a)/h ...."
    =============================
    Well sort of.
    The limit of that expression as s goes to zero is the instantaneous velocity. It is also the slope of your curve at t = 5.
    However the expression as you wrote it is the average velocity or slope of the curve between t = 2 and t = 5
    Therefore draw a slope and s value at t = 5
    To make it really simple, sketch a straight line with that slope from t = 2 to t = 6
    Of course the curve could take all kinds of twists and turns instead of what we sketched, but the basic idea is that at t = 5 the slope is the same as the slope of a straight line from t = 2 to t = 5

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