Solving a Problem: Car Speed When Driver Slammed Brakes

In summary, the car's brakes were applied and the net force was equal to the force of friction minus the applied force. So, the applied force was ma(applied). Then, using v(final)^2=v(initial)^2+2a(delta x), the initial velocity can be found.
  • #1
kbrowne29
12
0
I'm a bit confused as to how to finish this problem:
At an accident scene on a level road, inestigators measure a car's skid marks to be 88 m long. It was a rainy day and the coefficient of friction was estimated to be .42. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.

OK, here's what I can get. Using F=ma, I know the net force is equal to the force of friction minus the applied force. And so we get F(friction)-F(applied)=ma. We also know that F(friction)=
mu(kinetic)F(normal). And the normal force is equal to mg. And so the force of friction is mu(kinetic)mg. So, mu(kinetic)mg-force(applied)=ma. Now, the applied force can be rewritten as ma(applied). Now the mass can be canceled out of each term, and the result is: mu(kinetic)g-a(applied)=a. This is where I get stuck. I can't seem to figure out how to determine the applied acceleration. Once I get that, then using v(final)^2=v(initial)^2+2a(delta x), I can find the initial velocity. I would appreciate any help on this problem. Thanks.
 
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  • #2
Well, here's how I solved the problem:

The force of friction = μR

R = mg

So,

Friction = μmg

When the car's brakes are applied, the force causing the deceleration is equal to the force of friction, is it not?

Therefore

ma = μmg

And

a = μg

Then just use v^2 = u^2 + 2as, like you said.
 
  • #3
Originally posted by kbrowne29

OK, here's what I can get. Using F=ma, I know the net force is equal to the force of friction minus the applied force.
What "applied" force? The only horizontal force on the car is the friction of the road!
 
  • #4


Originally posted by Doc Al
What "applied" force? The only horizontal force on the car is the friction of the road!

That's exactly where I was going wrong. For some reason, I kept solving the problem as if the car were accelerating, not decelerating.
Thank you both for your help.
 

What is the process for solving a problem related to car speed when the driver slammed the brakes?

The process for solving a problem related to car speed when the driver slammed the brakes involves several steps. First, the researcher must gather all relevant data, such as the initial speed of the car, the distance traveled after the brakes were slammed, and the time it took for the car to come to a complete stop. Then, the researcher must analyze this data using mathematical equations and formulas to determine the car's deceleration rate. Finally, the researcher can use this information to calculate the car's initial speed before the brakes were slammed.

What factors can affect the car's speed when the driver slammed the brakes?

There are several factors that can affect the car's speed when the driver slammed the brakes. These include the initial speed of the car, the type and condition of the brakes, the weight and size of the car, the road conditions, and the driver's reaction time. Even small variations in these factors can have a significant impact on the car's speed and deceleration rate.

How can the car's speed when the driver slammed the brakes be calculated?

The car's speed when the driver slammed the brakes can be calculated using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration rate (which is equal to the deceleration rate in this case), and t is the time it took for the car to come to a complete stop. By rearranging this equation, the initial velocity (u) can be calculated by subtracting the product of the acceleration rate and time from the final velocity.

Why is it important to understand the car's speed when the driver slammed the brakes?

Understanding the car's speed when the driver slammed the brakes is crucial for several reasons. For one, it can help investigators or researchers reconstruct an accident or determine the cause of a crash. It can also provide valuable information for improving car safety and preventing accidents in the future. Additionally, understanding the physics behind a car's deceleration can help drivers make informed decisions and react appropriately in emergency situations.

What are some common mistakes made when solving a problem related to car speed when the driver slammed the brakes?

One common mistake when solving a problem related to car speed when the driver slammed the brakes is not considering all relevant factors, such as the weight of the car or the condition of the brakes. Another mistake is using incorrect formulas or equations, which can lead to inaccurate results. It is also essential to be aware of any assumptions being made and to ensure that they are valid. Finally, it is crucial to double-check all calculations and data to avoid errors and obtain reliable results.

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