Concept explainers
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
signify? Approximate this integral using the Midpoint Rule with five subintervals.
(e) Approximate the acceleration at t = 0.8
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Calculus of a Single Variable
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