Question

The force acting on a particle varies as in the figure. Find the work done by the force as the particle moves from x =0 m to x = 10.0 m.

• A. 30 J
• B. 27.0 J
• C. 24.0 J
• D. 21.0 J

Answer 1

The correct option is D

21.0 J

The work done on the particle by the force F as the particle moves from

$x=x_i$ to $x=x_f$ is the area under the curve from $x_i$ to $x_f$

For x=0 to 8.00 m

W=area of triangle ABC $=\frac{1}{2}AC\times altitude$

$W_{0-8}=\frac{1}{2}\left(8.00m\right)\left(6.00N\right)=24.0J$

For x=8.00 m to 10.0 m

$W_{8-10}=\frac{1}{2}\left(2.00m\right)(-3.00N)=-3.00J$

For x = 0 m to 10.0 m

$W_{0-10}=W_{0-8}+W_{8-10}$

=24.0 J + (-3.00 J) = 21.0 J