Question

While driving home at 136 km per hour from a spring break vacation in British Columbia, when you see a speed trap 100 meters ahead of you. Knowing that you'll get caught if you apply the brakes, you decide to coast and pray you slow down in time. Nevertheless, you get stopped, and a grinning mounty informs you that you were traveling at 110 kilometers per hour.

a. What was the force of friction on your 907kg car?

b. Assuming the speed limit was 100 kilometers per hour, what would have been the minimum force needed to keep you from getting caught?

Answer 1

here,

the initial speed , u = 136 km/h = 37.78 m/s

distance , s = 100 m

a)

final speed , v = 110 km/h = 30.56 m/s

let the acceleration be a

using the third equation of motion

v^2 - u^2 =2 * a * s

30.56^2 - 37.78^2 = 2 * a * 100

solving for a

a = - 2.47 m/s^2

mass ,m = 907 kg

the friction force , F = m * a

F = - 907 * 2.47 N = - 2240.29 N

b)

when final speed , v = 100 km/h = 27.78 m/s

let the acceleration be a

using the third equation of motion

v^2 - u^2 =2 * a * s

27.78^2 - 37.78^2 = 2 * a * 100

solving for a

a = - 3.28 m/s^2

mass ,m = 907 kg

the friction force , F = m * a

F = - 907 * 3.28 N = - 2974.96 N