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Math Help - Calc Word problem

  1. #1
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    Calc Word problem

    Can someone please help me out.

    Suppose a car is moving along straight road and distanct traveled t hours after starting from rest is given by f (t) = 2t^2+60t. Find the avg velocity of the car over the time intervals (0,2) and (1,2). Find the instanteaneous velocity at t = 1 and t = 2.

    Can someone explain hte process of how to solve this? Using the method equations of

    f (x+h) - f(x) / h

    Thanks
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  2. #2
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    The average velocity is the gradient of the line that joins \displaystyle (0,2) and \displaystyle (1,2).

    The instantaneous velocity is the gradient of a line that joins any point to another point extremely close to it. So for any point \displaystyle (x, f(x)), you can say that a point close to it is \displaystyle (x + h, f(x+h)), and the gradient would be \displaystyle \frac{f(x+h) - f(x)}{x+h-x} = \frac{f(x+h) - f(x)}{h}.


    So in your question, to evaluate the instantaneous velocity at \displaystyle t = 1, you know that on the curve, when \displaystyle t = 1, f(t) = f(1) = 62. A point close to this would be t = 1 + h, so \displaystyle f(t) = f(1 + h) = 2(1 + h)^2 + 60(1 + h).

    Simplify then put into your equation for the gradient.
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  3. #3
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    Sorry, but what does gradient mean? I'm still not sure how to solve the problem for the average one at least.
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  4. #4
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    Gradient means slope...
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