(1) A 0.20-mathrm(kg) hockey puck initially traveling 5.0 mathrm(~m) / mathrm(s) is pushed on ice by a hockey stick with a constant force of 7.0 mathrm(~N) over a distance of 8.0 mathrm(~m) . Friction is negligible. Determine the final velocity of the hockey puck.

To determine the final velocity of the puck, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.<br /><br />Given information:<br />- Force applied on the puck: 7.0 N<br />- Initial velocity of the puck: 5.0 m/s<br />- Distance traveled by the puck: 8.0 m<br /><br />Step 1: Calculate the work done on the puck.<br />Work = Force × Distance<br />Work = 7.0 N × 8.0 m = 56.0 J<br /><br />Step 2: Calculate the change in kinetic energy of the puck.<br />Change in kinetic energy = Work done<br />Change in kinetic energy = 56.0 J<br /><br />Step 3: Calculate the final velocity of the puck.<br />Initial kinetic energy = 1/2 × m × (initial velocity)^2<br />Final kinetic energy = 1/2 × m × (final velocity)^2<br />Change in kinetic energy = Final kinetic energy - Initial kinetic energy<br />56.0 J = 1/2 × m × (final velocity)^2 - 1/2 × m × (5.0 m/s)^2<br />56.0 J = 1/2 × m × (final velocity)^2 - 12.5 J<br />68.5 J = 1/2 × m × (final velocity)^2<br />(final velocity)^2 = 137 m^2/s^2<br />final velocity = √137 m/s ≈ 11.7 m/s<br /><br />Therefore, the final velocity of the puck is approximately 11.7 m/s.