Speedometer readings for a motorcycle at 12-second intervals are given in the table. t (s) 0 12 24 36 48 60 v (ft/s) 32 28 25 21 24 27 (a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals. 1884 x ft (b) Give another estimate using the velocities at the end of the time periods. 1512 x ft (c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain. (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t. (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t. (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
Speedometer readings for a motorcycle at 12-second intervals are given in the table. t (s) 0 12 24 36 48 60 v (ft/s) 32 28 25 21 24 27 (a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals. 1884 x ft (b) Give another estimate using the velocities at the end of the time periods. 1512 x ft (c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain. (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t. (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t. (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Speedometer readings for a motorcycle at 12-second intervals are given in the table.
t (s)
0
12 24 36 48 60
v (ft/s) 32 28 25 21 24 27
(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of
the time intervals.
1884
x ft
(b) Give another estimate using the velocities at the end of the time periods.
1512
x ft
(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.
(a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.
(a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of
t.
(b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
Enhanced Feedback
Please try again. To estimate the distance the motorcycle traveled during an interval of time, find an estimate for the area
under the velocity graph using rectangles.
Remember, using one-sided endpoints for a graph only gives an overestimate or underestimate when the graph only
increases or only decreases.
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