Question

You are driving at the speed of 26.3 m/s(58.844 mph) when suddenly the car in front of you (previously traveling at the samespeed) brakes and begins to slow down with the largest deceleration possible without skidding. Considering an average human reaction,you press your brakes 0.519 s later. You also brake and decelerate as rapidly as possible without skidding. Assume that the coefficient of static friction is 0.811 between both cars’wheels and the road.The acceleration of gravity is 9.8 m/s .

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

Answer 1

The acceleration of the car in front of you when it brakes is 7.978 m/s².

Step-by-step explanation:

To calculate the acceleration of the car in front of you when it brakes, we need to consider the deceleration caused by the maximum static friction between the car's tires and the road. This friction force can be calculated using the coefficient of static friction, which is given as 0.811. The deceleration is equal to the acceleration due to gravity, which is 9.8 m/s², multiplied by the coefficient of static friction.

The formula for calculating deceleration is:

a = μg

where a is the deceleration, μ is the coefficient of static friction, and g is the acceleration due to gravity.

Substituting the given values, we get:

a = (0.811)(9.8)

Solving for a, the acceleration of the car in front of you when it brakes is 7.978 m/s².