A block of mass 2 ~kg F(t) is free to move along the x -axis. It is at rest and from t=0 onwards it is subjected to a timedependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

Step-by-step solution

Change in momentum = area under F - t graph aligned p & = 1 2 4 3- 1 2 1.5 4 3 1.5 & [ Force at 4.5 ~s = 4 3 1.5 ~N ] & =6-1.5=4.5 ~kg ~m ~s aligned As p=m(v-u)=m v ( u=0) v= p m = 4.5 ~kg ~m ~s ⁻¹ 2 ~kg = 4.5 2 ~ms ⁻¹ Kinetic energy of the block after 4.5 ~s is K= 1 2 m v^2= 1 2 2 ~kg ( 4.5 2 ~ms ⁻¹ )^2=5.06 ~J