A car that weighs 1.1 × 10 4 N is initiallymoving at a speed of 36 km/h when the
ID: 1667064 • Letter: A
Question
A car that weighs 1.1 × 104 N is initiallymoving at a speed of 36 km/h when the brakes are applied and thecar is brought to a stop in 17 m. Assuming that the force thatstops the car is constant, find (a) themagnitude of that force and (b) the timerequired for the change in speed. If the initial speed is doubled,and the car experiences the same force during the braking, by whatfactors are (c) the stopping distanceand (d) the stopping time multiplied?(There could be a lesson here about the danger of driving at highspeeds.Explanation / Answer
The mass of the car (m) = W/g = 1.1 x 10^4/9.8 = 1122.45 Kg The initial velocity of car = 36 km/h = (36 x 1000)/3600 = 10m/sec Now let the retardation produced by brakes is a m/s^2,by:- v^2 = u^2 - 2as =>0 = 10 x 10 - 2 x a x 17 =>a = 100/34 = 2.94 m/s^2 (a) Force (F) = m x a =>F = 1122.45 x 2.94 = 3300 N (b) If the initial speed is doubled i.e. = 20 m/s, now let the carstops in s meter; by:- v^2 = u^2 - 2as =>0 = 20 x 20 - 2 x 2.94 x s =>s = 400/5.88 = 68 m (c) The stopping distance in IInd case = 68/17 = 4 x stoppingdistance in Ist case (d) Let the time taken to stop the car in Ist case is t1 & thetime taken to stop the car in IInd case is t2 sec, =>t1 = u/a & t2 = 2u/a =>t1 = 10/2.94 = 3.40 sec & t2 = 20/2.94 = 6.80 sec =>t2 = 2 x t1
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