Consider an old-fashion bicycle with a small wheel of radius 0.18 m and a large
ID: 1465512 • Letter: C
Question
Consider an old-fashion bicycle with a small wheel of radius 0.18 m and a large wheel of radius 0.71 m. Suppose the rider starts at rest, accelerates with a constant acceleration for 1.9 minutes to a velocity of magnitude 12 m/s. He maintains this velocity for 13.3 minutes and then decelerates, with a constant deceleration, for 3.7 minutes at which time he is at rest.
a. Find the total distance traveled by the rider. Give your answer in kilometers.
b. Find the total angle through which a point on the small wheel has turned.
c. Find the angular velocity of the wheel of radius 0.27 m during the constant velocity part of the trip.
Thank you!!
Explanation / Answer
let maximum velocity reached by rider be Vmax
Vmax = at
a = 12/(1.9* 60)
a = 0.105 m/s^2
so distance travelled along accelration
S = 0.5 at^2
S = 0.5 * 0.105 *(1.9* 60)^2
S = 682.89 m
distance travelled with constant velocity = 12 *13.3*60 = 9576 m
12 =3.6*60*(-a)
-a= 0.054 m/s^2 (decelration)
so distance = 12*12/(2*0.054) = 1333.34 m
total distance S = 682.89 + 9576 + 1333.34 = 11.59 km
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smalllest angle tunred theta = Wt
theta = (V/r(*t
theta = 12*1.9* 60)/071
theta = 19.26 radians
use angular Velocity W = V/r
W = 12/0.27
W = 44.44 rad/s