The variation of force F acting on a particle with its position x is represented by a straight line graph. The force increases linearly from 10 N at x = 0 to 30 N at x = 4 m . The work done by the force in moving the particle from x = 0 to x = 4 m is

Step-by-step solution

The work done by a variable force is equal to the area under the force-position ( F-x ) graph. The given graph is a straight line from (0, 10) to (4, 30) , which forms a trapezium with the x -axis. The parallel sides of the trapezium are F₁ = 10 N and F₂ = 30 N , and the perpendicular distance between them is x = 4 m . W = Area of trapezium = 1 2 (F₁ + F₂) x W = 1 2 (10 + 30) 4 W = 1 2 40 4 = 80 J Answer: 80 J