A car is traveling in a straight line for 1 hour. Its velocity v in miles per ho

Question

A car is traveling in a straight line for 1 hour. Its velocity v in miles per hour at six-minute intervals is shown in the table.

(a.) Produce a reasonable graph of the velocity function v by graphing these points and connecting them with a smooth curve.

(b.) Find the open intervals over which the acceleration a is positive.

(c.) Find the average acceleration of the car (in miles per hour squared) over the interval [0,0.4].

(e.) Approximate the acceleration at t = 0.8.

The only one I'm really having a problem with is (d.). I'm not sure how to divide the function into five subintervals. Please Help!!!

Explanation / Answer

You have hours from 0 to 1, so your five subintervals will be 0-0.2, 0.2-0.4, 0.4-0.6,0.6-0.8, and 0.8 to 1.0. The interval signifies the distance traveled over the hour. Using the tranpezoid rule we have 0.2/2 (0 +2*20 +2*60 +2*40+2*40+65)= 38.5 miles

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