A 65 kg student climbs a 3.0 m rope in 6.0 s at constant speed. Take g = 9.8 m/s². What is the student's average power output against gravity?

A motor lifts a 200 kg crate straight upward 8.0 m in 10 s at constant speed. Take g = 9.8 m/s². What average power does the motor deliver to the crate?

A worker pushes a crate with a constant 80 N force parallel to its motion for 12 m in 6.0 s. How much work does the worker do on the crate?

A rope pulls a sled with a constant 45 N force along the direction of motion for 20 m in 15 s. What is the average power delivered by the rope?

A 0.50 kg cart starts from rest on a frictionless track. A motor transfers 36 J of energy to it in 4.0 s. What speed does the cart reach?

A 12 kg backpack is lifted 1.5 m at constant speed in 3.0 s. Take g = 9.8 m/s². How much work is done against gravity?

A winch raises a 50 kg load 5.0 m in 8.0 s. If the winch is 80% efficient, what average input power is required? Take g = 9.8 m/s².

A 75 kg cyclist climbs a hill with a vertical rise of 40 m in 80 s at steady speed. Take g = 9.8 m/s². What average power goes into increasing gravitational potential energy?

A sled slides 18 m while friction exerts a constant 12 N force opposite the motion. The trip takes 9.0 s. How much mechanical energy is dissipated by friction?

A spring transfers 20 J of energy to a 0.25 kg cart in 0.50 s. What is the average power transferred during the launch?

A 0.40 kg ball is dropped from rest at 2.5 m above the floor and rebounds to 1.6 m. Take g = 9.8 m/s². How much energy is dissipated during the bounce?

A 0.80 kg toy car rolls from rest down a 1.2 m hill and then climbs only 0.75 m up the next hill. Take g = 9.8 m/s². How much mechanical energy was dissipated?

A 0.60 kg ball is thrown upward at 7.0 m/s and reaches a maximum height 2.0 m above its release point. Take g = 9.8 m/s². How much energy was dissipated by air resistance?

A spring stores 48 J of elastic potential energy. After launching a 1.0 kg cart across a rough patch, the cart moves at 8.0 m/s. How much energy was dissipated?

A 55 kg skier starts from rest and descends a vertical height of 12 m, reaching 12 m/s at the bottom. Take g = 9.8 m/s². How much mechanical energy is dissipated?

A 0.20 kg pendulum bob is released 0.50 m above its lowest point and later rises only 0.35 m on the other side. Take g = 9.8 m/s². How much energy was dissipated?

Use the energy chart. A sled's mechanical energy drops from the Start bar to the End bar while it travels 14 m. What average friction force acted on it?

Use the energy chart. A cart's mechanical energy drops from the Start bar to the End bar while it rolls 12 m across a rough floor. What is the average friction force on the cart?

Use the energy chart. A block slides 16 m while its mechanical energy changes from the Start bar to the End bar. What average friction force dissipated the energy?

Use the energy chart. A skier travels 25 m along a rough slope as mechanical energy changes from the Start bar to the End bar. What average friction force acted?

Use the energy chart. A crate slides 10 m, and its mechanical energy drops from the Start bar to the End bar. What average friction force dissipated the missing mechanical energy?

Use the energy chart. A scooter coasts 10 m while mechanical energy changes from the Start bar to the End bar. What average resistive force acted?

Use the force–distance graph. A 3.0 kg cart starts from rest on a frictionless track, and the force acts along the motion. What speed does it have at the end?

Use the force–distance graph. A 2.0 kg cart starts from rest on a frictionless level track. The force is along the motion. What is the cart's final speed?

Use the force–distance graph. A 1.5 kg cart starts from rest, friction is negligible, and the force points along the motion. What speed does the cart reach?

Use the force–distance graph. A 4.0 kg cart starts from rest on a frictionless track. The applied force is along the motion. What is the cart's speed at 10 m?

An elevator lifts a known mass through a known vertical height in a known time at constant speed. Which relationship gives the average power with the fewest extra quantities?

A varying horizontal force acts on a cart over a measured distance, and the cart starts from rest on a frictionless track. Which plan best finds the final speed?

A ball starts from rest at a known height and falls without air resistance. Which relationship finds its speed just before hitting the ground without needing the fall time?

A puck with known mass and initial speed slides to rest under a constant friction force. Which relationship directly gives the stopping distance?