Question

If a position dependent force $(3x^2 - 2x + 7)N$ acting on a body of mass 2 kg displaces it from $x = 0\, m$ to $x = 5\, m$, then the work done by the force is

• A. 165 J
• B. 115 J
• C. 150 J
• D. 135 J

Hint:

For position-dependent forces, work done is calculated by integrating the force function with respect to displacement over the limits of movement.

Answer 1

The Correct Option is D

Work done by a variable force is given by: \[ W = \int_{x_1}^{x_2} F(x) \, dx \] Given force: \( F(x) = 3x^2 - 2x + 7 \) N, displacement from \(x=0\) to \(x=5\). Calculate the integral: \[ W = \int_0^5 (3x^2 - 2x + 7) \, dx = \left[x^3 - x^2 + 7x\right]_0^5 = (125 - 25 + 35) - 0 = 135\, \text{J} \] So, the work done by the force is 135 J.