A car that weighs 1.0 × 10^4 N is initially moving at a speed of 37 km/h when th

Question

A car that weighs 1.0 × 10^4 N is initially moving at a speed of 37 km/h when the brakes are applied and the car is brought to a stop in 17 m. Assuming that the force that stops the car is constant, find (a) the magnitude of that force and (b) the time required for the change in speed. If the initial speed is doubled, and the car experiences the same force during the braking, by what factors are (c) the stopping distance and (d) the stopping time multiplied? (There could be a lesson here about the danger of driving at high speeds.)

Explanation / Answer

Weight of the car W = 1 x 10 4 N Mass of the car m = W / g                              = 1020.4kg Initial speed u = 37 km / h                        = 37 x 1000 m / 3600 s                        = 10.277 m / s Stoping distance S = 17 m Final speed v = 0 From work energy theorem work = change in kinetic energy                                               FS = ( 1/ 2) m[ v 2 - u 2]                                                  F = - 3170.22 N (b). Time t = ( V - u ) / a Where a = acceleration                = F / m                = - 3.106 m/ s 2 So, t = 3.307 s (c). Initial speed U = 2u                              = 20.554 m / s Force F = 3170.22 N Work done = change in kinetic energy              FS ' = ( 1/ 2) m[ v 2 - U 2]                S ' = -215332.9385 / 3170.22 Stopping distance S ' = 67.92 m Time t = ( v - U ) / a           = 6.614 s                         

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