High School

We appreciate your visit to You are driving at a speed of 34 1 m s 76 2958 mph when suddenly the car in front of you previously traveling at. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

You are driving at a speed of 34.1 m/s (76.2958 mph) when suddenly the car in front of you (previously traveling at the same speed) brakes. Considering an average human reaction time, you press the brakes 0.536 s later. Assume that the brakes on both cars are fully engaged and that the coefficient of friction is 0.799 between both cars and the road. The acceleration of gravity is 9.8 m/s².

Calculate the magnitude of the acceleration of the car in front of you when it brakes. Provide your answer in units of m/s².

Answer :

Final answer:

The magnitude of the acceleration of the car in front of you when it brakes is 63.62 m/s².

Explanation:

To calculate the magnitude of the acceleration of the car in front of you when it brakes, we can use the equation:

a = (v_f - v_i) / t,

where a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and t is the time.

First, let's find the initial velocity of the car in front of you. Since both cars are traveling at the same speed, the initial velocity of the car in front of you is also 34.1 m/s.

Next, we need to find the final velocity of the car in front of you. We can use the equation:

v_f = v_i + a*t,

where v_f is the final velocity, v_i is the initial velocity, a is the acceleration, and t is the time. Plugging in the given values, we get:

v_f = 0 + a*0.536 s.

Substituting this expression for v_f into the first equation, we get:

a = (v_f - v_i) / t = (a*0.536 s - 34.1 m/s) / 0.536 s.

Simplifying the equation, we have:

a = 34.1 m/s / 0.536 s

= 63.62 m/s².

Therefore, the magnitude of the acceleration of the car in front of you when it brakes is 63.62 m/s².

Thanks for taking the time to read You are driving at a speed of 34 1 m s 76 2958 mph when suddenly the car in front of you previously traveling at. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada