A 65kg Bicyclist rides 88kg bicycle with a speed of 40m/s. (a) How much work mus

Question

A 65kg Bicyclist rides 88kg bicycle with a speed of 40m/s. (a) How much work must be done by the brakes to bring the bike and rider to a stop? (b) how far does the bicycle travel if it takes 4.0 second to come to rest? (c) What is the magnitude of the braking force?

Explanation / Answer

a) we know that work done = change in kinetic energy                                     W = KE 2 - KE1                                          = 0 - 0.5 mv2                                          = 0 - 0.5 * (65 + 88) (40)2                                          = - 244800 J b) the acceleration of the Bicyclist is                      v = u + at                     ==> a = - u / t = -40/4 = - 10.0m/s2      Therefore the distance traveled        S = u t + 0.5at2           = 40 * 4 -0.5 * 10 * 4 * 4           = 160 -80           = 80 m c) workdone = F . S       ==> F = W / S                 = - 244800 / 80                 = - 3060N

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