Question

If the force acting on a body is inversely proportional to its speed, the kinetic energy of the body is

• A. constant
• B. directly proportional to time
• C. inversely proportional to time
• D. directly proportional to square of time

Hint:

Force inversely proportional to speed means constant power, so work done grows linearly with time.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
If \(F\propto\dfrac{1}{v}\), then \(F=\dfrac{k}{v}\) and the power \(P=Fv=k\) is constant.

Step 2: Apply Newton's second law
\(m v\dfrac{dv}{dt}=k\), so \(v\,dv=\dfrac{k}{m}dt\).

Step 3: Integrate
Starting from rest, \(\dfrac{v^2}{2}=\dfrac{k}{m}t\), so \(v^2=\dfrac{2kt}{m}\).

Step 4: Kinetic energy
\(KE=\dfrac{1}{2}mv^2=kt\), which is directly proportional to time. This is option (B).

Final Answer:
The kinetic energy is directly proportional to time. \[ \boxed{\text{(B) }\text{directly proportional to time}} \]