in a shuffleboard game, the puck slides a total of 12 m before coming to rest. if the coefficient of friction is 0.21, what was the initial speed?

7.03m/s

how?

how?

what will be when the distance is 5 m and, coefficient of kinetic friction equal to 0.1?

To find the initial speed of the puck in the shuffleboard game, we can use the concept of work and kinetic energy. The work done on the object is equal to the change in kinetic energy.

The work done by friction can be calculated using the formula:

Work = Frictional force × Distance

The frictional force can be calculated using the equation:

Frictional force = coefficient of friction × Normal force

In this case, let's assume that the normal force is equal to the weight of the puck. Therefore, the frictional force becomes:

Frictional force = coefficient of friction × Weight

Next, we need to calculate the work done by friction. The formula for work is:

Work = Force × Distance

However, in this case, the work done by friction is negative since it acts in the opposite direction of the displacement. So, the work done by friction can be calculated as:

Work = (-1) × Frictional force × Distance

Now, equating this to the change in kinetic energy, we get:

(-1) × Frictional force × Distance = Change in kinetic energy

Since the puck comes to rest, the change in kinetic energy is equal to the initial kinetic energy. Thus,

(-1) × Frictional force × Distance = (1/2) × Mass × Initial velocity^2

Given that the distance is 12 m, the coefficient of friction is 0.21, and you need to calculate the initial velocity, we now have:

(-1) × (0.21) × (12) = (1/2) × Mass × Initial velocity^2

Finally, you'll need to provide the mass of the puck to solve for the initial speed. Once the mass is known, the equation can be rearranged to solve for the initial velocity.