Lesson 3 of 10 · 7 min
Kinetic energy and the work-energy theorem
NCERT § "Notions of Work and Kinetic Energy: The Work-Energy Theorem"
On the stage, Kiran shoves a 40 kg crate of prasadam tins so it slides at 4 m/s and lets go. It stops after 2 m. Shoved at 8 m/s, it goes not 4 m but 8 m. Why four times as far for twice the speed?
The lesson in notes
In short
Kinetic energy of a body of mass m moving at speed v is K = ½mv², a non-negative scalar.
In terms of momentum, K = p²/2m; so at equal momentum the lighter body has more kinetic energy.
Work-energy theorem: the net work done on a body by all forces equals the change in its kinetic energy, K_f − K_i = W_net.
The theorem follows from the second law combined with the kinematics, and it is a scalar statement, so directions enter only through the signs of the work terms.
Doubling speed makes kinetic energy four times larger; a 30% rise in momentum raises kinetic energy by 69% since K ∝ p² for fixed mass.
A body sliding to rest on a rough floor loses all its kinetic energy to the negative work of friction: ½mv² = μ_k m g d, so the stopping distance d = v²/(2μ_k g) does not depend on mass.