A 1.5-kg physics textbook is initially at rest on a steel table.The textbook is then pushed with a constant force of 3.0 N. Friction with a magnitude of 1.8 N is exerted on the moving book by the surface of the table.Use the equations for work and kinetic energy to calculate the final velocity of the textbook after it has been pushed 1.0 meter across the table.

## Step 1The problem involves the principles of work and kinetic energy. The work done on an object is equal to the change in its kinetic energy. The work done by a force is calculated by the formula:### \(W = F \cdot d \cdot \cos(\theta)\)where is the work done, is the force, is the distance, and is the angle between the force and the direction of motion.## Step 2In this case, the force is applied in the same direction as the motion, so and \(\cos(\theta) = 1\). Therefore, the work done by the applied force is:### ## Step 3The work done by the frictional force is negative because it opposes the motion. The work done by the frictional force is:### ## Step 4The total work done on the textbook is the sum of the work done by the applied force and the work done by the frictional force:### ## Step 5The change in kinetic energy of the textbook is equal to the total work done on it:### ## Step 6The kinetic energy of an object is given by the formula:### where is the mass of the object and is its velocity.## Step 7We can rearrange the formula to solve for the velocity:### ## Step 8Substituting the given values into the formula, we get:###