A body of mass 0.5 kg travels in a straight line with velocity v =a x3/2 where a = 5 m¯¹/2 s¯¹. What is the work done by the net force during its displacement from x = 0 to x = 2 m ?
Given mass of body is 0.5 kg , equation of velocity is v = a x 3 2 , acceleration is a = 5 m 2 / s and the displacement is x = 0 to x = 2 m .
Initial velocity u of the body is given by x = 0 ,
u = 5 × ( 0 ) 3 2 = 0 m / s
Final velocity v of the body is given by x = 2 m ,
v = 5 × ( 2 ) 3 2 = 10 2 m / s
Change in kinetic energy Δ K is given by,
Δ K = 1 2 m ( v 2 − u 2 )
Substitute the values in the above expression.
Δ K = 1 2 ( 0.5 ) × [ ( 10 2 ) 2 − 0 2 ] = 50 J
The change in kinetic energy will be stored as work done by the net force.
Hence, work done by the net force during the given displacement is 50 J .
Given mass of body is
Initial velocity
Final velocity
Change in kinetic energy
Substitute the values in the above expression.
The change in kinetic energy will be stored as work done by the net force.
Hence, work done by the net force during the given displacement is
