A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.210 and the push imparts an initial speed of 3.50 m/s?

(in m)

To find the distance the box will go, we can use the concept of work and energy. The work done by the push will be equal to the work done by the friction force, which will cause the box to stop.

The work done by the push is given by the equation:

Work = Force x Distance

The force exerted by the push can be calculated using Newton's second law:

Force = Mass x Acceleration

In this case, the box is already in motion, so the force required to keep it moving is equal to the force opposing its motion due to friction. The frictional force can be calculated using the equation:

Frictional Force = Coefficient of Kinetic Friction x Normal Force

The normal force is the force exerted by the floor on the box, which is equal to the weight of the box:

Normal Force = Mass x Gravitational Acceleration

Once we have the frictional force, we can calculate the work done by the friction force using the equation mentioned earlier. Setting the work done by the push equal to the work done by friction will give us the distance the box will go, as the box will stop when the two forces are equal.

Let's calculate the distance:

1. Calculate the force exerted by the push:
- Mass of the box is not given, so we cannot calculate the force.

Unfortunately, we need the mass of the box to calculate the force and hence, the distance. Without the mass information, it is not possible to determine how far the box will go.