A sports car skids to a stop, leaving skid marks 290 m long.
If the coefficient of kinetic friction between tires and pavement is 0.80, how fast was the car going before the skid?
To find the speed of the car before the skid, we can use the relationship between the distance traveled, the coefficient of friction, and the initial speed of the car.
The formula for the distance traveled during a skid stop is given by:
d = (v^2) / (2 * u * g)
Where:
- d is the distance traveled (in this case, the length of the skid marks, which is 290 m)
- v is the initial speed of the car
- u is the coefficient of kinetic friction
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Rearranging this formula, we can solve for v:
v = √(2 * u * g * d)
Now, let's substitute the given values into the formula and calculate the speed:
v = √(2 * 0.80 * 9.8 * 290)
= √(5.88 * 9.8 * 290)
= √(17111.2)
≈ 130.7 m/s
Therefore, the car was going approximately 130.7 m/s before the skid.