Question

A body initially at rest is acted upon by a constant force \( F \) for time \( t \). The kinetic energy at time \( t \) is

• A. \( \dfrac{F^2 t^2}{m} \)
• B. \( \left(\dfrac{Ft}{m}\right)^2 \)
• C. \( \dfrac{Ft}{2m} \)
• D. \( \dfrac{F^2 t^2}{2m} \)

Hint:

For constant force problems, always find velocity first using \( v = at \), then apply kinetic energy formula.

Answer 1

The Correct Option is D

Step 1: Use Newton’s second law.
A constant force \( F \) acting on a mass \( m \) produces acceleration \[ a = \frac{F}{m} \]
Step 2: Find velocity after time \( t \).
Since the body starts from rest, \[ v = at = \frac{F}{m} t \]
Step 3: Write expression for kinetic energy.
\[ K = \frac{1}{2} m v^2 \]
Step 4: Substitute the value of velocity.
\[ K = \frac{1}{2} m \left(\frac{Ft}{m}\right)^2 = \frac{F^2 t^2}{2m} \]
Step 5: Conclusion.
The kinetic energy of the body at time \( t \) is \( \dfrac{F^2 t^2}{2m} \).