Question

Some of the following equations are kinematic equations, where the symbols have their usual meaning. The work-energy theorem is represented by

• A. $v = u + at$
• B. $s = ut$
• C. $s = ut + \frac{1}{2}at^2$
• D. $v^2 = \frac{u^2}{2} + as$
• E. $v^2 = u^2 + 2as$

Hint:

The equation $v^2 = u^2 + 2as$ is particularly useful because it is time-independent, much like the Work-Energy Theorem itself.

Answer 1

Answer: (E)

Concept:
The Work-Energy Theorem states that the net work done on an object is equal to its change in kinetic energy: \[ W_{net} = \Delta K = \frac{1}{2}mv^2 - \frac{1}{2}mu^2 \]

Step 1: Deriving the kinematic equivalent.
Using Newton's Second Law ($F = ma$) and the definition of work ($W = Fs$): \[ mas = \frac{1}{2}mv^2 - \frac{1}{2}mu^2 \] Dividing the entire equation by $m$ and multiplying by 2: \[ 2as = v^2 - u^2 \implies v^2 = u^2 + 2as \]

Step 2: Identifying the equation.
This equation represents the conservation of energy in kinematic terms, where $2as$ relates to the work done and $v^2-u^2$ relates to the change in energy.