Four students write down the no-time kinematic equation from memory. Who has it right?
A 4 kg cart rolls across a smooth floor at 2 m/s. For the next 3 m, the net force on it is a steady 8 N, forward.
That is +24 J of net work.
The work-energy theorem promises that those 24 J land in the cart's kinetic energy, exactly. Why there, and nowhere else?
Well, start with what a net force does: it accelerates. The net force is 8 N on 4 kg, so the acceleration is 8 / 4 = 2 m/s².
The kinematics topic already links speed to distance when no clock is needed: v² = v0² + 2aΔx. That equation is reused here, not rebuilt.
Substitute the cart's numbers. The gained term 2aΔx is (2 × 2 × 3), which is 12. So v² = 4 + 12 = 16: the cart leaves the stretch at 4 m/s.
Now count the kinetic energy at each end: ½ × 4 × (2 × 2) is 8 J at the start, and ½ × 4 × (4 × 4) is 32 J at the end.
The gain is 32 - 8 = 24: the cart's kinetic energy rose by 24 J, exactly the net work done.
A sled speeds up as a net force acts on it across some distance. Why does the net work land in the sled's kinetic energy?
The theorem is not a new law. It is W = Fd chained with the dynamics topic's F = ma and the kinematics topic's no-time equation.
And if the forces on an object balance, the net force is zero: zero net work, and the kinetic energy does not change.
The forces on a moving delivery robot balance along a stretch of hallway. State what happens to its kinetic energy over that stretch, and the reasoning.
Balanced forces make the net force zero.
A zero net force does zero net work.
Net work is the change in kinetic energy, so a zero change means no change.
The robot's kinetic energy stays the same over the stretch.
An elevator rises at a steady 3 m/s, the forces on it balancing. Is net work being done on the elevator?
Exactly two horizontal forces act on a wagon over one stretch: one does +30 J of work, the other does -12 J. By how much does the wagon's kinetic energy change?
The works add: 30 - 12 = 18, so the net work is +18 J.
Net work shows up as kinetic energy, joule for joule.
The wagon's kinetic energy rises by exactly 18 J.
Zeke says: a box's kinetic energy rises by exactly 15 J whenever the net work on it is +15 J, however many forces act. Is Zeke right?
A subway train gains speed as a net force acts on it along the track. Which statement explains why the net work on the train equals its kinetic energy change?
A pickup truck cruises along a flat, straight highway at a steady speed, the forces on it balancing. Which statement is right?
Exactly two horizontal forces act on a go-kart along one stretch: one does +26 J of work, the other does -6 J. What happens to the go-kart's kinetic energy over the stretch?