Before completing this question, you may want to remind yourself of the definiti

Question

Before completing this question, you may want to remind yourself of the definitions and functional notation translations of average trip speed and average speed on an interval. Reread Section 1 (Introduction to Speed and Rates of Change) and Section 5 (Three Languages) of the Supplement. A car moves along a straight road so that its distance traveled (in miles) at t minutes is given by the formula D(t-t-0.025e NOTE: Some of the following questions require you to enter units. If the units are "miles per minute," enter "miles per minute" or "mi/min." a.) How far does the car travel during the first 16 minutes? Include units b.) what is the car's average trip speed at 11 minutes? Do not round your answer. Include units. C.) Find a formula for the car's average trip speed at time t minutes. Simplify. (Your formula should be linear) ATS(t) = d.) Find the time at which the car's average trip speed is 0.8 miles per minute. Include units. e.) Compute the car's average speed from t=6 to 11 minutes. Do not round your answer. Include units. f.) Find a formula for the car's average speed during the 5-minute interval beginning at time t minutes. Simplify as much as possible. (Your formula should be linear.) g.) Find a 5-minute interval during which the average speed of the car is exactly 0.8 miles per minute. from t to minutes

Explanation / Answer

a)

distance car travelled in 16 minutes =D(16)

distance car travelled in 16 minutes =(16 -0.025*162)

distance car travelled in 16 minutes =(16 -0.025*162)

distance car travelled in 16 minutes =9.6 miles

b)

average trip speed =[(11 -0.025*112)-(0 -0.025*02)]/(11-0)

average trip speed =0.725 miles per minute

c)

ATS(t)=[(t -0.025t2)-(0 -0.025*02)]/(t-0)

ATS(t)=(1 -0.025t)

d)

ATS(t)= 0.8

1-0.025t =0.8

=>0.025t=0.2

=>t=8

at 8 minutes average trip speed is 0.8miles per minute

e)

average speed =[(11 -0.025*112)-(6 -0.025*62)]/(11-6)

average speed =0.575 miles per minute

f)

average speed =[((t+5) -0.025(t+5)2)-(t -0.025t2)]/((t+5)-t)

average speed =[t+5 -0.025(t+5)2 -t +0.025t2]/(5)

average speed =0.875-0.05t

g)

average speed =0.8 miles per minute

=>0.875-0.05t=0.8

=>t=(0.875-0.8)/0.05

=>t=1.5

interval , t=1.5 to 1.5+5

interval , t=1.5 to 6.5 minutes

please rate if helpful. please comment if you have any doubt

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