A box is set into motion from rest and comes to rest in 5.0 s. If the coefficient of kineticfriction is 0.45, what was the box’s initial velocity?

To solve this problem, we need to use the equations of motion. However, we are not given the distance the box travels, so we need to find a way around that. We know that the force of friction is what brings the box to a stop, so we can use that to find the acceleration, and then use the acceleration to find the initial velocity.

Here are the steps:

1. First, we need to find the acceleration of the box. The force of friction is given by the equation F = μN, where μ is the coefficient of friction and N is the normal force. In this case, the normal force is just the weight of the box, so we can say that F = μmg, where m is the mass of the box and g is the acceleration due to gravity.

2. The force of friction is also equal to the mass of the box times its acceleration (F = ma), so we can set these two equations equal to each other and solve for a: μmg = ma. The mass cancels out, leaving us with a = μg.

3. Plug in the given value for μ (0.45) and the acceleration due to gravity (9.8 m/s^2) to find a: a = 0.45 * 9.8 = 4.41 m/s^2. This is the acceleration of the box.

4. Now we can use the equation v = u + at to find the initial velocity of the box, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. The box comes to rest, so its final velocity is 0. Rearranging the equation gives us u = v - at.

5. Plug in the values we know: u = 0 - (4.41 m/s^2 * 5.0 s) = -22.05 m/s.

6. The negative sign indicates that the box was moving in the opposite direction of the acceleration, which makes sense because the box was slowing down. So, the initial velocity of the box was 22.05 m/s.