11. In an accident a freeway sports car made skid marks 200 m long along the pavement. The police estimated the braking acceleration of the car to be – 0.8g under the road conditions prevailing. Determine the speed of the sports car when the brakes were applied.
Kinetic energy loss equals work done against skidding friction. The mass M cancels out.
The friction force F can be deduced from the mass and acceleration.
(M/2) V^2 = (0.8g)*M*X
V^2 = 1.6 *g*200
V = 56 m/s = 201.6 km/s = 125 mph
To determine the speed of the sports car when the brakes were applied, we can use the physics equation that relates distance, acceleration, and initial velocity:
v^2 = u^2 + 2ad
where:
v = final velocity (speed of the car when the brakes were applied)
u = initial velocity (unknown)
a = acceleration (braking acceleration of the car)
d = distance (length of the skid marks)
We know the values of a and d. We need to solve this equation for u.
First, let's substitute the values into the equation:
0 = u^2 + 2(-0.8g)(200)
Now, we need to simplify the equation using values from known constants:
0 = u^2 - 160g
Next, let's solve for u by isolating it:
u^2 = 160g
Taking the square root of both sides:
u = √(160g)
Now, we need to substitute the value of g, which is the acceleration due to gravity (approximately 9.8 m/s^2):
u = √(160 * 9.8)
u ≈ √(1568)
u ≈ 39.6 m/s
Therefore, the speed of the sports car when the brakes were applied is approximately 39.6 m/s.