Question

A force \( F \) is applied on a body of mass \( m \) so that the body starts moving from rest. The power delivered by the force at time \( t \) is proportional to:

• A. \( t \)
• B. \( t^2 \)
• C. \( t^3 \)
• D. \( \sqrt{t} \)

Hint:

Instantaneous power delivered by a constant force is: \[ P = F \cdot v \] If the object starts from rest, velocity increases linearly with time \( (v = at) \), so power becomes proportional to time: \[ P \propto t \]

Answer 1

The Correct Option is A

Step 1: Use Newton’s second law.
The body starts from rest under constant force \( F \), so acceleration is: \[ a = \frac{F}{m} \] Step 2: Velocity at time \( t \) From the equation of motion: \[ v = u + at = 0 + \frac{F}{m}t = \frac{F}{m}t \] Step 3: Instantaneous power delivered by the force \[ P = F \cdot v = F \cdot \left( \frac{F}{m}t \right) = \frac{F^2}{m}t \] Step 4: Proportionality
Since \( P = \frac{F^2}{m} t \), power is directly proportional to \( t \), hence: \[ P \propto t \]