Summary of "Work Energy Theorem: ICSE CLASS X ,XI CBSE/ ISC :WORK 05 : Work Done = Change in Kinetic Energy ;"

Work–Energy Theorem

Definition of work (reminder): W = F · s = F s cosθ, where θ is the angle between force and displacement.
Kinetic energy (KE): KE = 1/2 m v². (The video focuses only on kinetic energy.)
Work–Energy Theorem (central statement):

The net work done on an object equals the change in its kinetic energy.
- In formula form: W = ΔK = K_final − K_initial = 1/2 m v² − 1/2 m u².
- This holds whether kinetic energy increases or decreases (work can be positive or negative).

Positive work: force and displacement in the same direction (e.g., gravity does positive work when an object falls).
Negative work: force opposite to displacement (e.g., catching a moving ball — your force opposes the ball’s motion, so work done on the ball is negative and KE decreases).

Using the theorem you can compute the work done without directly knowing force or displacement — just use the initial and final speeds and the mass.
Units: work and kinetic energy are measured in joules (J).

Given:

Compute change in kinetic energy:

Conclusion: Work done on the block = 150 J (without needing F or s).

Start with ΔK = 1/2 m (v² − u²).
Factor out m/2: ΔK = (m/2)(v² − u²).
Use the kinematic identity v² − u² = 2 a s (where a is acceleration and s is displacement).
Substitute: ΔK = (m/2) × (2 a s) = m a s.
Recognize m a = F (Newton’s second law), so ΔK = F s = work.

Therefore net work = change in kinetic energy (W = ΔK).

The net work done by the net force changes an object’s kinetic energy by exactly that amount.
The theorem applies for both increases and decreases in kinetic energy; the sign depends on the direction of force relative to displacement.
It provides a convenient way to find work when forces or displacements are unknown but speeds and mass are known.
Work and kinetic energy share the same units: joules (J).