Concept:Newton's Second Law and Kinematics can be used to find the final velocity, which is then substituted into the Kinetic Energy equation.
Formula:$$ a = \frac{F}{m} \quad \text{and} \quad v = u + at \quad \text{and} \quad K.E = \frac{1}{2}mv^2 $$
Solution:- Acceleration \( a = \frac{P}{m} \) (where Force is labeled P).
- Since it starts from rest (\( u = 0 \)), final velocity is \( v = at = \left(\frac{P}{m}\right)t \).
- Kinetic Energy \( K.E = \frac{1}{2}mv^2 \).
- Substitute \( v \): \( K.E = \frac{1}{2}m\left(\frac{Pt}{m}\right)^2 = \frac{1}{2}m \left(\frac{P^2t^2}{m^2}\right) \).
- Simplify to get: \( K.E = \frac{P^2t^2}{2m} \).
Why other options are incorrect:Option A forgets the \( 1/2 \) factor in the kinetic energy formula. Options C and D introduce incorrect fractional coefficients not present in derivation.
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