Work-Energy Method: Solving Doubled Initial Speed of Car

W = 1/2(m)(2v)^2 - 1/2(m)(v)^2= 1/2(m)(4v^2 - v^2)= 1/2(m)(3v^2)= 3/2(m)(v^2)Thus, the stopping distance is directly proportional to the square of the initial velocity. In summary, the stopping distance is directly proportional to the square of the initial velocity and is given by the equation W = 3/2(m)(v^2). Therefore, if the initial speed
  • #1
Heat
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[SOLVED] Work-Energy Method

Homework Statement



A car is stopped by a constant friction force that is independent of the car's speed. By what factor is the stopping distance changed if the car's initial speed is doubled? (Solve using work-energy methods.)

Homework Equations



Wtotal = delta K

The Attempt at a Solution



From what the problem is stating, is that friction force, is separate from car's speed.
''if the car's initial speed is doubled?''
K1 = 1/2(m)(2v)^2

I know the answer is 4, but I don't comprehend, what is the car's initial speed is tripled, would it be 6?
 
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  • #2
How does stopping distance relate to kinetic energy?
 
  • #3
well if the velocity is higher, then it would be harder to stop at a shorter distance than a long one.
 
  • #4
I'm looking for a precise answer. What factors affect stopping distance? Give an equation.
 
  • #5
well

W = F*s

s being distance

and work total = k2-k1

so, k2-k1 = F*s
 

FAQ: Work-Energy Method: Solving Doubled Initial Speed of Car

How does the work-energy method solve for the doubled initial speed of a car?

The work-energy method uses the principle of conservation of energy to solve for the doubled initial speed of a car. This principle states that the total energy of a system remains constant, and can be transferred between different forms, such as kinetic energy and potential energy. By calculating the initial and final energies of the car, the work-energy method can determine the change in speed.

What information is needed to use the work-energy method?

In order to use the work-energy method to solve for the doubled initial speed of a car, you will need to know the mass of the car, the distance it travels, and any external forces acting on the car, such as friction or air resistance. You will also need to know the initial and final speeds of the car.

Can the work-energy method be used for any type of motion?

Yes, the work-energy method can be used for any type of motion, as long as the principle of conservation of energy applies. This includes both linear and rotational motion. However, the calculations may be more complex for rotational motion.

How accurate is the work-energy method in determining the doubled initial speed of a car?

The work-energy method is a highly accurate method for determining the doubled initial speed of a car. This is because it takes into account all forms of energy, including potential and kinetic energy, as well as external forces. However, the accuracy of the method may be affected by factors such as measurement errors or assumptions made in the calculations.

Are there any limitations to using the work-energy method?

One limitation of the work-energy method is that it only considers the initial and final states of the car, and does not take into account the motion of the car in between. This means that it may not accurately predict the speed of the car at any given point during its motion. Additionally, the method may not be suitable for situations where there are significant changes in external forces or non-conservative forces, such as collisions or explosions.

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