Suppose an object is moving with constant acceleration, a,

Chapter 8, Problem 8.6.27

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Suppose an object is moving with constant acceleration, a, and its motion is initially observed at a moment when its velocity is v0. We set time, t, equal to 0, at this point when velocity equals v0. Then its velocity t seconds after the initial observation is V(t) at v0. (Note that the product of acceleration and time is velocity.) Now suppose we want to find its average velocity between time 0 and time t. The average velocity can be measured in two ways. First, we can find the average of the initial and final velocities by calculating a numerical average or mean; that is, we add the two velocities and divide by 2. So, between time 0 and time t, (1) We can also find the average velocity by dividing the change in distance by the change in time. Thus, between time 0 and time t, (2) If we substitute the expression for average velocity (from time 0 to time t) given by Equation (1) into Equation (2), we get (3) We know that V(t) at v0. Substitute this expression for V(t) in Equation (3) and solve for d. Interpret your results. 28