11. 3 points Prvous Answes SCakET8 5 1503XP 4/5 Submissions used Speedometer rea
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11. 3 points Prvous Answes SCakET8 5 1503XP 4/5 Submissions used 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 27 25 21 24 28 (a) Estimate the distance traveled by the motorcycle during this time period using the velooities at the beginning of the time intervals (b) Give another estimate using the velocities at the end of the time periods (c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain. (ays a lower estimate and (b) is an upper estimate since v is an ncreasing function of t. (b) is a lover estimate and (a) is an upper estimate since v is a decreasing function of. since v is neither an increasing nor decreasing function of t v (a) and (b) are neither lower nor upper estimates Nod Help?Tr ommandopnExplanation / Answer
Sol:-WE will be using Riemann Sum for this problem. Note that to find the distance, the formula would be d=v*t.
A) This problem states for us to use the BEGINNING of the time intervals. This is like a left-hand riemann sum. Therefore, you would use all the values except for the last one when t(s)=60. Since they are all spaced out within a 12 second time interval, We will be multiplying all the values by 12. The velocity is not constant, and it does not have a specific pattern. so We will have to multiply 12 to each value as listed.
12(32) + 12(27) + 12(25) + 12(21) + 12(24) =1548
OR
S = 12 ( 32 + 27 + 25 + 21 + 24 ) =1548
Either way, WE will come up with the same answer.1548 should be our answer.
B) This problem is exactly like part A, but it is asking for the END of the time period. Therefore, We will be doing a right-hand riemann sum.
12(27) + 12(25) + 12(21) +12(24) + 12(28) =1500
OR
S= 12 ( 27 + 25 + 21 + 24 + 28 )
WE should end up with the answer 1500.
C neither lower nor upper .
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