Question

A body of mass 8 kg is moved by a force \(F = 3x\) N, where x is the distance covered. Initial position is x = 2 m and the final position is x = 10 m. The initial speed is zero. The final speed is

• A. 6 m/s
• B. 12 m/s
• C. 18 m/s
• D. 14 m/s

Hint:

For variable force, integrate \(F\,dx = m v\,dv\).

Answer 1

The Correct Option is A

To solve this problem, we need to determine the final speed of the body given that the force applied is a function of distance. We will use the Work-Energy Principle, which states that the work done by all forces acting on a body is equal to the change in its kinetic energy.

1. **Expression for Work Done**:
   • The given force is \(F = 3x\) N.
   • Work done \((W)\) can be calculated by integrating the force over the distance traveled, from the initial position \(x_1 = 2\) m to the final position \(x_2 = 10\) m:
   • Evaluating the integral:
2. **Application of Work-Energy Principle**:
   • According to the Work-Energy Principle,
   • Substituting the given values, \(m = 8 \text{ kg}, u = 0 \text{ m/s (initial speed)},\) and \(W = 144 \text{ Joules}\):
   • Solve for \(v^2\):
   • Therefore, the final speed \(v\) is:
3. **Conclusion**:
   • The final speed of the body is 6 m/s, which matches the given correct option.