Consider an old-fashion bicycle with a small wheel of radius 0.17 m and a large wheel of radius 0.92 m. Suppose the rider starts at rest, accelerates with a constant acceleration for 2.7 minutes to a velocity of magnitude 10 m/s. He maintains this velocity for 13.7 minutes and then accelerates, with a constant deceleration, for 4.1 minutes at which time he is at rest. Find the total distance traveled by the rider. Give your answer in kilometers.

10259.6 m

Explanation:

We are given that

Radius of small wheel,r=0.17 m

Radius of large wheel,r'=0.92 m

Initial velocity,u=0

Time,t=2.7 minutes=162 s

1 min=60 s

Velocity,v=10m/s

Time,t'=13.7 minutes=822 s

Time,t''=4.1 minutes=246 s

Substitute the values

Substitute the values

Total distance traveled by rider=s+s'+s''=809.6+8220+1230=10259.6 m

Explanation:

Given

initial velocity of bicycle,

velocity of the bicycle after the first phase of acceleration,

duration of first phase of uniform acceleration,

duration of second phase of zero acceleration,

uniform velocity during the second phase,

duration third phase of uniform deceleration,

final velocity after the third phase of motion,

Now using the equation of motion:

is the distance covered in the first phase of motion.

Now using the equation of motion:

is the distance covered in the third phase of motion.

Hence the total distance covered by the bicycle in the whole incident is: