A car that weighs 1.5 × 104 N is initially moving at a speed of 36 km/h when the

Question

A car that weighs 1.5 × 104 N is initially moving at a speed of 36 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.) (a) Number (b) Number (c) Number (d) Number Click if you would like to Show Work for this question: Units Units Units Units Open Show Work

Explanation / Answer

(a) U^2 = 2aS. where U the initial velocity, a the acceleration and S is the distance travelled. V the final velocity = 0.

U = 36km/h = 36*10 /36 = 10 m/s/

a = U^2/ 2S = - 10^2 / 2*17 = 2.94 m/s^2.

Force = ma = (1.5e4/9.8)*(2.94) = 4502 N

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(b) V = U - at

0= 10 - (2.94) t

=> t = 3.4s

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(c)

Force remains the same; the acceleration will be the same. S will change in proportion to the square of the initial velocity U. S = U^2 / a Since U is doubled S will be 2*2 = 4 times the previous one.

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(d) Since acceleration is the same,

Time t = initial velocity / acceleration. Since initial velocity is doubled, time will be doubled.

The multiplication factor is 2.

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