A 2kg object accelerated as a net force acts on it. During the 5 seconds this force acts, the object velocity changes from 3 m/s east to 7m/s west. The initial kinetic energy of the object was 9 joules, and the final kinetic energy was 49 joules

The force is 4N to the west direction,

Explanation:

Let's define east as +x, and west as -x

The mass of the object is 2 kg.

During 5 seconds, the velocity changes from 3m/s to -7m/s

Now, by the second law of Newton we have that:

F = m*a

This means that the applied force is equal to the mass times the acceleration, and we also know that the integral of the acceleration is equal to the velocity:

a(t) = F/m

v(t) = F/m*t + v0

where v0 is the initial speed, in this case, 3m/s

v(t) = (F/m)*t + v0

at t = 5s, we know that the velocity is -7m/s

-7m/s = (F/2kg)*5s + 3m/s

-10*(2/5)N = F

-4N = F

This means that the force is 4N in the west direction.

The final statement about the kinetic energy does not give any information, because:

k = (1/2)*n*v^2

then  

initial energy = (1/2)*2kg*(3m/s)^2 = 9 j

final energy = (1/2)*2kg(-7m/s)^2 = 49 J

the area between the graph and the t axis