(a) -10 J
The graph represents the force versus the position of the particle: this means that the area under the graph represent the work done on the particle.
Therefore, let's start by calculating the area. The area of the trapezium between x = 0 and x = 3 m is:
While the area of the triangle between x = 3 m and x = 6 m is
So, the work done on the particle is
(b) 40 J
The kinetic energy of the particle is given by
where
m is its mass
v is its speed
The mass of the particle is
m = 0.250 kg
While the initial speed is
v = 20.0 m/s
So the initial kinetic energy (at x = 6 m) is
For the work-energy theorem, the final kinetic energy of the particle (at x=0) will be the initial kinetic energy + the work done by the force on it, therefore: