A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 m is:

According to the work-energy theorem,

$$\text{Work done}=\Delta KE$$

$$W=KE_{\text{final}}-KE_{\text{initial}}$$

The particle starts from rest, therefore

$$KE_{\text{initial}}=0$$

Work done is equal to the area under the F-x graph.

From the graph:

Rectangle area:

$$2\times2=4$$

Trapezium area:

$$\frac{1}{2}(2+3)\times1=2.5$$

Therefore,

$$W=4+2.5$$

$$W=6.5\ \text{J}$$

Hence,

$$KE_{\text{final}}=6.5\ \text{J}$$

$$\boxed{6.5\ \text{J}}$$