Calculate the acceleration of the car in front of you when it brakes

Question

You are driving at the speed of 25.1 m/s (56.1591 mph) when suddenly the car in front of you (previously traveling at the same speed) brakes and begins to slow down with the largest deceleration possible without skidding. Considering an average human reaction, you press your brakes 0.432 s later. You also brake and decelerate as rapidly as possible without skidding. Assume that the coefficient of static friction is 0.899 between both cars’ wheels and the road. The acceleration of gravity is 9.8 m/s 2 . Calculate the acceleration of the car in front of you when it brakes. Answer in units of m/s 2 .

Answer 1

Interesting problem. Since the initial velocity and time is given but not the final velocity nor the d.istance. Since the coefficient of friction, µ is given then that is the clue to finding the car's acceleration.

µ = F_f / F_N where F_f is the friction force and F_N is the normal force. Since the weight W is equal to the F_N or

W = F_N because since these two forces are the only verticle forces and their sum is zero. Now F_f =µF_N and

W = mg so µmg = F_f but F_f = ma also or µg = a. This becomes a = (0.899)(9.8 m/s² ) = 8.8 m/s² .

Lastly, one cannot forget that F_f is in the opposite direction of motion and the acceleration a is really a deceleration or a = -8.8 m/s² .