A) The particle will come to rest instantaneously, at t = 6.8 s.
B) The final velocity of the particle will be 18m/s,
C) Work done by the force on the particle is 375 J.
D) All of the above
Correct Answer: C
Solution :
Initial velocity of the particle is along positive X-axis and force is also acting along positive X-axis for, \[t=1\] to \[t=4\] s, so particle will never come to rest upto \[t=4\] s, the velocity of the particle will change but then onwards, velocity becomes constant. Now, from impulse-momentum theorem, \[m{{v}_{f}}-m{{v}_{i}}=\int{F\,\,dt}\] \[\Rightarrow \] \[2\times {{v}_{f}}-2\times 5=\frac{1}{2}\,\times 20\times 3\] \[\Rightarrow \] \[{{v}_{f}}=20\,\,m/s\]and from work energy theorem, \[\frac{mv_{f}^{2}}{2}-\frac{mv_{i}^{2}}{2}=\] Work done by force (W) \[\Rightarrow \] \[W=\frac{2\times {{20}^{2}}}{2}-\frac{2\times {{5}^{2}}}{2}=375\,J\]
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