Speedometer readings for a motorcycle at 12-seconds interval are given in table.

Question

Speedometer readings for a motorcycle at 12-seconds interval are given in table. (a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals. ft (b) Give another estimate using the velocities at the end of the time periods. ft (c) Are your estimates in parts (a) and (b) upper and lower estimates? Explains. (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t. (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.

Explanation / Answer

Solution:

0 at 12s average v = (32 + 28)/2 = 30ft/s---- e = v* t = 30 * 12 = 360 ft
12 at 24s average v =( 28 + 25)/2 = 26.5ft/s-----e = v* t = 26.5 * 12 = 318 ft
24 at 36s average v=( 25 + 22)/2 = 23.5ft/s ----e = v * t = 23.5 * 12 = 282 ft
36 at 48s average v= (22 + 25)/2 = 23.5ft/s------e = v * t = 23.5 * 12 = 282 ft
48 at 60s average v = (25 + 27)/2 = 26ft/s---------e = v* t = 26 * 12 = 312 ft

distance traveled = 360 + 318 + 282 + 282 + 312 = 1554ft

a )
0 at 12 --- e = v * t = 32 * 12 = 384 ft
12 at 24 ---e = v * t = 28 *12 = 336 ft
24 at 36 ---e = v * t = 25 * 12 = 300 ft
36 at 48 ---e = v * t = 22 * 12 = 264 ft
48 at 60----e = v * t = 25 * 12 = 300ft

distance traveled = 384+336+300+264+300 = 1584 ft

b)
0 at 12 --- e = v * t = 28 * 12 = 336 ft
12 at 24 ---e = v * t = 25 *12 = 300 ft
24 at 36 ---e = v * t = 22 * 12 = 264 ft
36 at 48 ---e = v * t = 25 * 12 = 300 ft
48 at 60----e = v * t = 27 * 12 = 324 ft
distance traveled = 1524 ft

average distance traveled = (1584 + 1524) / 2 = 1554 ft

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