Calculate the acceleration of the car in front of you when it brakes. Answer in units of m/s 2 .

Question

You are driving at the speed of 33.6 m/s (75.1771 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 0.428 s later. You also brake and decelerate as rapidly as possible without skidding. Assume that the coefficient of static friction is 0.779 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

First, let's calculate the deceleration of your car:

Initial speed (u) = 33.6 m/s

Final speed (v) = 0 m/s (since you come to a stop)

Time (t) = 0.428 seconds

You can use the formula:

v=u+at

Solving for acceleration (a)

0=33.6+a(0.428)

a=-33.6/0.428 m/s²

a=−78.5047m/s²

Now, we need to find the deceleration of the car in front. We'll use the concept of friction and the maximum deceleration without skidding.

Maximum static friction (F _friction) can be calculated using the formula:

F _friction =coefficient of friction×normal force

The normal force (F _normal ) is equal to the weight of the car, which can be calculated as:

F _normal=mass×gravity

Given:

Coefficient of static friction (μ) = 0.779

Acceleration due to gravity (g) = 9.8 m/s²

Now, we can calculate the normal force:

F _normal =mass×g

However, we need to convert your speed from mph to m/s. 75.1771 mph is approximately 33.6 m/s (as given).

So, let's calculate the deceleration of the car in front:

F _friction =μ× F _normal

a _{front car}= F _{friction /( mass of the front car)}

Now, we have all the values to calculate

a _{front car}=0.779×{(mass of the front car) × 9.8}/(mass of the front car)

The mass of the front car cancels out, and you are left with the deceleration due to friction, which is the acceleration of the front car:

a _{front car}=0.779×9.8m/s

a _{front car} ≈ 7.6422 m/s²

So, the acceleration of the car in front when it brakes is approximately

7.6422m/s ² .

Therefore, the acceleration of the car in front is 7.6422m/s² .