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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 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 ??

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2 Answers

Amritesh Raj
17 Points
4 years ago
Area under F-t graph = Change in momentum.Delta P = 1/2 * 4 *3 -1/2 *4/5 * 1.5= 4.5 kg m/sK = P^2 /2M K = 5.06 joule
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

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 = 0.5​(4)(3) − 0.5​(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 ​= Pf^2/2m​​
⟹ Kf​ = (4.5)2/2(2) ​= 5.06J

Thanks and Regards

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