(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:
[tex]A_1 = \frac{1}{2}(3+2)\cdot (-10)=-25[/tex]
While the area of the triangle between x = 3 m and x = 6 m is
[tex]A_2 = \frac{1}{2}(3\cdot 10)=15[/tex]
So, the work done on the particle is
[tex]W=A_1 + A_2 = -25 +15 = -10 J[/tex]
(b) 40 J
The kinetic energy of the particle is given by
[tex]K=\frac{1}{2}mv^2[/tex]
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
[tex]K_i = \frac{1}{2}(0.250)(20)^2=50 J[/tex]
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:
[tex]K_f = K_i + W = 50 + (-10) = 40 J[/tex]
