REASONING Let us assume that the skater is moving horizontally along the axis. The time it takes for the skater to reduce her velocity to from can be obtained from one of the equations of kinematics: The initial and final velocities are known, but the acceleration is not. We can obtain the acceleration from Newton's second law in the following manner. The kinetic frictional force is the only horizontal force that acts on the skater, and, since it is a resistive force, it acts opposite to the direction of the motion. Thus, the net force in the direction is , where is the magnitude of the kinetic frictional force.

Therefore, the acceleration of the skater is .

The magnitude of the frictional force is (Equation 4.8), where is the coefficient of kinetic friction between the ice and the skate blades and is the magnitude of the normal force. There are two vertical forces acting on the skater: the upward-acting normal force and the downward pull of gravity (her weight) . Since the skater has no vertical acceleration, Newton's second law in the vertical direction gives (taking upward as the positive direction) . Therefore, the magnitude of the normal force is and the magnitude of the acceleration is