Textbook Problem

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

t (hours)	0	0.1	0.2	0.3	0.4	0.5
v (mi/h)	0	10	20	40	60	50

t (hours)	0.6	0.7	0.8	0.9	1.0
v (mi/h)	40	35	40	50	65

(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 per hour) over the interval [0, 0.4].

(d) What does the integral

${\displaystyle {\int }_0^{1}v(t)}dx.$

signify? Approximate this integral using the Midpoint Rule with five subintervals.

(e) Approximate the acceleration at t = 0.8