The only force acting on a 2.0 kg body as it moves along the x - axis varies as shown in the figure. The velocity of the body at x = 0 is 4.0 $\frac{m}{s}$ What is the maximum K.E attained by the body between x=0 and x=5 m?

The correct option is A

12 J

Kinetic energy of the body at x = 0 is $K_1=\frac{1}{2}\times 2.0\times (4.0{)}^2=16.0j$

Work done by the force on the body is given by area bounded by the curve and x-axis.From x = 0 to x = 1.0m

The force decreases linearly from F = 4N to F = 0, but it is directed along +x-axis, work done by the force is +ve.For 1.0m < x $\le$ 5.0m, the force is -ve, so it is directed along -x axis for any interval in this region, the work done by the force will be -ve.

From x = 0 to x = 3.0m, work done by the force on the body = Area of the bounded region

$W_{net}=\frac{1}{2}\times 4\times 1.0-\frac{1}{2}\times 4\times 1.0=-4.0N.m=-4J$

Let the K.E of the body at x = 3.0 m be $K_3$

From work - energy theorem,

-4 = $K_3-16$

$K_3=12J$