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Question:

A block of mass 2kg is free to move along the x-axis. It is at rest and from t=0 onwards it is subjected to a time-dependent 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:

4.50 J

7.50 J

5.06 J

14.06 J

Solution:

Area under the F−t graph gives the change in momentum of the block. Area A= Area of triangle ABO - Area of triangle DCO ∴A=1/2(4)(3) − 1/2(2)(1.5)=4.5 Ns Initial momentum of the block Pi=0 Using A=Pf−Pi ⇒Pf=4.5 Ns Thus final kinetic energy of the block Kf=Pf²/2m ⇒Kf=(4.5)²/2(2)=5.06J