This is a practice problem. Consider an old-fashion bicycle with a small wheel o

Question

This is a practice problem.

Consider an old-fashion bicycle with a small wheel of radius 0.25 m and a large wheel of radius 0.86 m. Suppose the rider starts at rest, accelerates with a constant acceleration for 1.4 minutes to a velocity of magnitude 9 m/s. He maintains this velocity for 12.8 minutes and then decelerates, with a constant deceleration, for 3.4 minutes at which time he is at rest. Find the total distance traveled by the rider. Give your answer in kilometers.

I already know the correct answer, so please just explain!

Explanation / Answer

let maximum velocity reached by rider be Vmax

Vmax=9 = 1.4*60* a

a= 0.107 m/s^2

so distance travelled along accelration = 0.5*0.107*(1.4*60)^2 = 377.496

distance travelled with constant velocity = 9*12.8*60 = 6912 m

9= 3.4*60*(-a)

-a= 0.044 m/s^2 (decelration)

so distance = 81/(2*0.044) = 920.45

total distance = 377.496+6912+920.45=8209.946 m = 8.209 KM

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