A car that weighs 1.1 × 10 4 Nis initially moving at a speed of 42 km/h when the

Question

A car that weighs 1.1 × 104 Nis initially moving at a speed of 42 km/h when the brakes areapplied and the car is brought to a stop in 18 m. Assuming that theforce that stops the car is constant, find (a) themagnitude of that force and (b) the time requiredfor the change in speed. If the initial speed is doubled, and thecar experiences the same force during the braking, by what factorsare (c) the stopping distance and(d) the stopping time multiplied? (There could bea lesson here about the danger of driving at high speeds.)

Answer a: the tolerance is +/-2%
Answer b: the tolerance is +/-2%
Answer c: the tolerance is +/-2%
Answer d: the tolerance is+/-2%

Pls providecorrect units...
A car that weighs 1.1 × 104 Nis initially moving at a speed of 42 km/h when the brakes areapplied and the car is brought to a stop in 18 m. Assuming that theforce that stops the car is constant, find (a) themagnitude of that force and (b) the time requiredfor the change in speed. If the initial speed is doubled, and thecar experiences the same force during the braking, by what factorsare (c) the stopping distance and(d) the stopping time multiplied? (There could bea lesson here about the danger of driving at high speeds.)

Answer a: the tolerance is +/-2%
Answer b: the tolerance is +/-2%
Answer c: the tolerance is +/-2%
Answer d: the tolerance is+/-2%
Pls providecorrect units...

Explanation / Answer

weight w = 1.1 × 104 N, mass m = w/g initial velocity v = 42 km/h = 42/3.6 m/s final velocity v' = 0 displacemenr d = 18 m. acceleration = a v'2 - v2 = 2ad, so a =-v2/(2d) force F = ma = -mv2/(2d) = -wv2/(2gd) (a) the magnitude of that force iswv2/(2gd) = 4.24 × 103 N (b) the time required for the change in speed is t= (v' - v)/a = -v/a = 2d/v = 3.09 s If the initial speed is doubled, and the car experiences the sameforce during the braking, by what factors are (c)the stopping distance From F = wv2/(2gd), if F is the same, v is doubled, dwill increase to 4d, so answer: by the factor 4 and (d) the stopping time multiplied From t = 2d/v, if d becomes 4d, v becomes 2v then t becomes 2t, soanswer: by the factor 2

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