During the investigation of a traffic accident that occurred in a 25 m/s zone, police find skid marks 60.0 m long corresponding to the distance the car traveled while braking to a halt. They determine that the coefficient of friction between the car's tires and the roadway to be 0.50 for the prevailing conditions. Was the car speeding when it began to slide? Determine the speed of the car when the brakes were applied.
friction force = -.5 m g
= .5 (9.81) m = -4.9 m
a = F/m = -4.9 m/s^2
average speed during stop = Vi/2
so 60 = (Vi/2)t
120 = Vi t
Vi = 120/t
60 = Vi t - .5(4.9) t^2
60 = 120 - 2.45 t^2
t = 7 seconds
Vi = 120/7 = 17.1 m/s
To determine if the car was speeding and to find the speed of the car when the brakes were applied, we can use the concept of kinetic friction and the equation that relates the stopping distance, coefficient of friction, and initial velocity.
First, we need to calculate the stopping time of the car. We can use the equation:
Stopping distance = (initial velocity^2) / (2 * coefficient of friction * acceleration due to gravity)
Rearranging this equation, we can solve for the initial velocity:
Initial velocity = sqrt(2 * coefficient of friction * acceleration due to gravity * stopping distance)
Given:
- Stopping distance (d) = 60.0 m
- Coefficient of friction (μ) = 0.50
- Acceleration due to gravity (g) = 9.8 m/s^2
Substituting these values into the equation, we can calculate the initial velocity:
Initial velocity = sqrt(2 * 0.50 * 9.8 * 60.0)
Simplifying this calculation:
Initial velocity ≈ 34.64 m/s
Therefore, the speed of the car when the brakes were applied was approximately 34.64 m/s.
Now, to determine if the car was speeding when it began to slide, we compare the initial velocity (34.64 m/s) with the given speed limit (25 m/s). Since the initial velocity is higher than the speed limit, we can conclude that the car was indeed speeding when it began to slide.