Answer to Question #290164 in Physics for Matty

Question

Gabby is driving her 2400kg Mercedes on a rainy night (Oh, no…!) at a constant rate of 83km/hr when she sees a tree branch lying across the road 60 meters ahead and applies the brakes in a hurry (there will be some skidding involved, I fear). The coefficient of kinetic friction is 0.41.

1. Will Gabby stop before hitting the branch? What will the actual stopping distance be? 
2. How much time will be required to stop? 
3. What will be the average deceleration rate?

Answer 1

1. Find the kinetic energy and see how much work against friction this energy can perform. This will help us to find the stopping distance:

$$\dfrac12mv^2=\mu mgx,\\\space\\ x=\dfrac{v^2}{2\mu g}=66\text{ m}.$$

2. The time:

$$t=2x/v=5.7\text{ s}.$$

3. The average deceleration:

$$a=v^2/(2x)=\mu g=4.02\text{ m/s}^2.$$