You are driving at the speed of 31.8 m/s (71.1498 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 0.569 s later. You also brake and decelerate as rapidly as possible without skidding. Assume that the coefficient of static friction is 0.825 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

acceleration = g * (friction coefficient)

Why did the car apply for a job at the circus? Because it wanted to become a brake dancer!

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

a = (v_f - v_i) / t

Where:
a = acceleration
v_f = final velocity
v_i = initial velocity
t = time

Given:
v_i = 31.8 m/s
t = 0.569 s

Since the car in front of you is braking and slowing down, the final velocity (v_f) will be 0 m/s. Plugging in these values into the formula, we have:

a = (0 - 31.8 m/s) / 0.569 s

Simplifying the equation:

a ≈ -55.99 m/s^2

So, the acceleration of the car in front of you when it brakes is approximately -55.99 m/s^2.

To calculate the acceleration of the car in front when it brakes, we can use the following steps:

Step 1: Convert the speed of the car in front from mph to m/s.
71.1498 mph = 31.8 m/s

Step 2: Calculate the time it takes for you to react and apply the brakes.
Time taken to react (t) = 0.569 s

Step 3: Determine the distance traveled by the car in front during your reaction time.
Distance traveled in reaction time (d1) = initial speed x reaction time
d1 = 31.8 m/s x 0.569 s

Step 4: Calculate the new relative speed between your car and the car in front after your reaction time.
Relative speed after reaction time (Vr) = initial speed - distance traveled in reaction time
Vr = 31.8 m/s - (31.8 m/s x 0.569 s)

Step 5: Determine the maximum static friction force between the wheels and the road.
Maximum static friction force (Fs) = coefficient of static friction x weight of the car
Fs = 0.825 x weight of the car

Step 6: Calculate the deceleration of the car in front using Newton's second law of motion.
Deceleration (a) = Fs / mass of the car
a = Fs / mass of the car

Step 7: Set the deceleration equal to the relative speed divided by the reaction time to find the acceleration.
a = Vr / t

Now we have all the necessary information to calculate the acceleration of the car in front.

Note: Additional information, such as the weight of the car and the mass of the car, is required to provide an exact numerical answer.

To calculate the acceleration of the car in front when it brakes, we need to find the maximum deceleration it can achieve without skidding.

First, let's find the maximum deceleration possible without skidding for both cars. The maximum deceleration is equivalent to the value of static friction between the car's wheels and the road. We can calculate it using the coefficient of static friction (μs) and the acceleration due to gravity (g):

Maximum deceleration = μs * g

Given that the coefficient of static friction is 0.825 and the acceleration due to gravity is 9.8 m/s^2, we can calculate:

Maximum deceleration = 0.825 * 9.8 = 8.07 m/s^2

Now, let's find the deceleration of the car in front when it brakes. Remember that both cars were initially traveling at the same speed, and you pressed your brakes 0.569 seconds later.

The change in velocity (Δv) for the car in front, due to its braking, is given by:

Δv = a * t

Where a is the deceleration and t is the time between the car in front braking and you responding.

From the problem statement, you press the brakes 0.569 seconds after the car in front brakes, so t = 0.569 s.

Now we can determine the change in velocity:

Δv = a * t
Δv = ? * 0.569 (we need to find a)

Since both cars were initially traveling at the same speed, Δv is the change in velocity for only the car in front. This can be calculated by subtracting your initial velocity from the car in front's velocity:

Δv = 0 - 31.8 (since you're braking immediately)

Using the equation above, we can now solve for a:

Δv = a * t
-31.8 = a * 0.569

Solving for a:

a = -31.8 / 0.569 ≈ -55.93 m/s^2

The negative sign indicates that the car in front is decelerating (slowing down).

Therefore, the acceleration of the car in front of you when it brakes is approximately -55.93 m/s^2.