A car moving at 35 mi/h is stopped by jamming on the brakes and locking the wheels. The car skids 53 ft before coming to rest. How far would the car skid if it were initially moving at 56 mi/h?
The skid distance depends upon the kinetic energy, which is proportional to V^2.
(56/35)^2 * 53 = ?? ft.
To find out how far the car would skid if it were initially moving at 56 mi/h, we can use the concept of kinetic friction and the equations of motion. Here's how you can calculate it:
1. Convert the initial velocity from miles per hour to feet per second.
- Since 1 mile is equal to 5280 feet and 1 hour is equal to 3600 seconds, you can convert 56 mi/h to ft/s as follows:
56 mi/h * (5280 ft/1 mi) * (1 h/3600 s) = 82.67 ft/s (rounded to two decimal places)
2. The equation that relates distance (d), initial velocity (u), final velocity (v), acceleration (a), and time (t) is:
v^2 = u^2 + 2ad
3. In this case, the car comes to rest in the skid (v = 0), and the initial velocity (u) is given as 82.67 ft/s. We need to find the distance (d) the car will skid.
4. Rearrange the equation to solve for distance (d):
d = (v^2 - u^2) / (2a)
5. Since the car is skidding and the wheels are locked, the friction force acting on the car is the maximum static friction (μs) between the tires and the road multiplied by the car's weight (mg).
Note: We'll need to assume a value for the coefficient of static friction (μs). Let's say μs = 0.7, although different surfaces can have different coefficients.
6. Rewrite the formula for acceleration (a) as:
a = μs * g
where g is the acceleration due to gravity (approximately 32.2 ft/s^2).
7. Plug in the values into the equation for distance (d):
d = (0^2 - 82.67^2) / (2 * 0.7 * 32.2)
8. Calculate the distance (d):
d = (-6814.7289) / (45.08)
d = 151.34 ft (rounded to two decimal places)
Therefore, if the car were initially moving at 56 mi/h, it would skid approximately 151.34 feet before coming to rest.