Question

The speed limit on a particular city street is 45 miles per hour (which is 20 m/s). A driver approaching a stop light slams on their brakes, locking the wheels of their car in place so that they no longer rotate.

Part A

If the coefficient of friction between the car's tires and the street is 0.9, what is the minimum distance the driver would need to start braking in order to stop before the intersection?

Part B

When it rains, the coefficient of friction drops to 0.6. If the driver still wants to be able to stop in the same distance as in part A, what is the maximum speed they can have when it rains?

Answer 1

Part A.

Given that Initial speed of vehicle, U = 20 m/s

de-acceleration of vehicle due to friction will be:

a = -*g = -0.9*9.81 = -8.83 m/s^2

V = final speed of car = 0 m/s

Now Using 3rd kinematic equation:

V^2 = U^2 + 2*a*d

d = minimum stopping distance = (V^2 - U^2)/(2*a)

d = (0^2 - 20^2)/(2*(-8.83))

d = 22.65 m

Part B.

Now during rain, acceleration of vehicle will be:

a1 = -1*g = -0.6*9.81 = -5.89 m/s^2

Now when stopping distance is same as part A (d = 22.65 m), then max initial speed of vehicle will be:

Using 3rd kinematic equation:

V1^2 = U1^2 + 2*a1*d

V1 = final speed of vehicle = 0 m/s

U1 = sqrt (V1^2 - 2*a1*d)

U1 = sqrt (0^2 - 2*(-5.89)*22.65)

U1 = 16.33 m/s = max speed at which vehicle can drive during rains