( a ) 36 J ( b ) 15.75 J
Explanation:
In this case a body of 18 kg is placed on the smooth surface .
The distance covered covered by the body in four seconds can be found by the relation S = u t + 1/2 a t²
Here S is the displacement , u is the initial velocity and a is the acceleration of the body . t is the time taken
In this case initial velocity u = 0 , because the body is at rest .
the acceleration is force/mass = 9/18 = 0.5 m/sec²
The values are substituted in the above equation
Thus S = 0 + 1/2 x 0.5 x ( 4 )² = 4 m
Therefore the body will move 4 m in four seconds
The work done = Force x displacement
= 9 x 4 = 36 J
The displacement in fourth second can be found by relation
S₄ = u + a/2 ( 2 n - 1 ) ; where n is the number of seconds , which is 4 in this case
Thus S₄ = 0 + 0.5/2 ( 2 x 4 - 1 ) = 3.5/2 = 1.75 m
Therefore the work done = 9 x 1.75 = 15.75 J
