To solve this problem, we need to use the equations of motion and the concept of friction.

1. First, we need to understand that the stopping force is provided by the friction between Allison's shoes and the skateboard. The force of friction (F) can be calculated using the equation F = μN, where μ is the coefficient of friction and N is the normal force. In this case, since Allison is on a level road, the normal force is equal to her weight, which is mass (m) times gravity (g). So, F = μmg.

2. The work done by the friction force to stop Allison is equal to the change in her kinetic energy. The work done by a force is given by the equation W = Fd, where d is the distance. The kinetic energy of an object is given by the equation KE = 1/2 mv^2, where v is the velocity. So, we have the equation μmgd = 1/2 mv^2.

3. We can solve this equation for v, the initial velocity. First, cancel out the mass on both sides, then multiply both sides by 2, and finally take the square root of both sides to get v = sqrt(2μgd).

4. Now we can plug in the given values: μ = 0.450, g = 9.8 m/s^2 (the acceleration due to gravity), and d = 13.1 m.

5. So, v = sqrt(2*0.450*9.8*13.1) = 12.1 m/s.

Therefore, the maximum velocity Allison could have initially been travelling is 12.1 m/s.

Question

To solve this problem, we need to use the equations of motion and the concept of friction.

1. First, we need to understand that the stopping force is provided by the friction between Allison's shoes and the skateboard. The force of friction (F) can be calculated using the equation F = μN, where μ is the coefficient of friction and N is the normal force. In this case, since Allison is on a level road, the normal force is equal to her weight, which is mass (m) times gravity (g). So, F = μmg.

2. The work done by the friction force to stop Allison is equal to the change in her kinetic energy. The work done by a force is given by the equation W = Fd, where d is the distance. The kinetic energy of an object is given by the equation KE = 1/2 mv^2, where v is the velocity. So, we have the equation μmgd = 1/2 mv^2.

3. We can solve this equation for v, the initial velocity. First, cancel out the mass on both sides, then multiply both sides by 2, and finally take the square root of both sides to get v = sqrt(2μgd).

4. Now we can plug in the given values: μ = 0.450, g = 9.8 m/s^2 (the acceleration due to gravity), and d = 13.1 m.

5. So, v = sqrt(2*0.450*9.8*13.1) = 12.1 m/s.

Therefore, the maximum velocity Allison could have initially been travelling is 12.1 m/s.

Knowee AI · Accepted Answer

To solve this problem, we need to use the equations of motion and the concept of friction.

1. First, we need to understand that the stopping force is provided by the friction between Allison's shoes and the skateboard. The force of friction (F) can be calculated using the equation F = μN, where μ is the coefficient of friction and N is the normal force. In this case, since Allison is on a level road, the normal force is equal to her weight, which is mass (m) times gravity (g). So, F = μmg.

2. The work done by the friction force to stop Allison is equal to the change in her kinetic energy. The work done by a force is given by the equation W = Fd, where d is the distance. The kinetic energy of an object is given by the equation KE = 1/2 mv^2, where v is the velocity. So, we have the equation μmgd = 1/2 mv^2.

3. We can solve this equation for v, the initial velocity. First, cancel out the mass on both sides, then multiply both sides by 2, and finally take the square root of both sides to get v = sqrt(2μgd).

4. Now we can plug in the given values: μ = 0.450, g = 9.8 m/s^2 (the acceleration due to gravity), and d = 13.1 m.

5. So, v = sqrt(2*0.450*9.8*13.1) = 12.1 m/s.

Therefore, the maximum velocity Allison could have initially been travelling is 12.1 m/s.

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