Answer to Question #96415 in Mechanics | Relativity for Nyx

Question

You are driving at the speed of 33.4 m/s
(74.7296 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 0.437 s later. You also
brake and decelerate as rapidly as possible
without skidding. Assume that the coefficient
of static friction is 0.829 between both cars’
wheels and the road.
The acceleration of gravity is 9.8 m/s2.
Calculate the acceleration of the car in front
of you when it brakes.
Answer in units of m/s2.
Don't round answer

Answer 1

$$ma=\mu mg$$

The acceleration is

$$a=\mu g=(0.829)(9.8)=8.1242\frac{m}{s^2}$$