Question

A body of mass 8kg is moved by a force where x is the distance covered. Initial position is x=2m and final position is x=10m. If initially the body is at rest, the final speed is

Answer 1

Answer:

Work done = Change in Kinetic energy

initial kinetic energy = 0

Work done can be found by integrating, as the force is dependent on instantaneous position.

So,

Work done = Integral from x=2 to x=10 of 3x dx

= 3x^2/2 from x=2 to x= 10 , after calculation this comes out to be = 144 Joules

So, Final kinetic energy = 144 J, since initial kinetic energy = 0 J

And, hence,

1/2 mv^2 = 144 J

or,

1/2(8)v^2 = 144 J

v^2 = 36

or,

v = 6 m/s Hope this helps you ! ｡◕‿◕｡