Question

A block of mass 2 kg 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

• A. 4.50 J
• B. 7.50J
• C. 5.06 J
• D. 14.06J

Answer 1

Answer: (C)

5.06 J

Answer 2

Area under the $F - t$ graph gives the change in momentum of the block. Area $A =$ Area of triangle $ABO$ - Area of triangle DCO $\therefore A =\frac{1}{2}(4)(3)-\frac{1}{2}(2)(1.5)=4.5 N s$ Initial momentum of the block $P _{ i }=0$ Using $A = P _{ f }- P _{ i }$ $\Longrightarrow P _{ f }=4.5 Ns$ Thus final kinetic energy of the block $K _{ f }=\frac{ P _{ f }^{2}}{2 m }$ $\Longrightarrow K _{ f }=\frac{(4.5)^{2}}{2(2)}=5.06 J$