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Work Power and Energy question

2019 · 8 Apr · Shift 1 · Q53
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Work Power and Energy question

2019 · 8 Apr · Shift 1 · Q53

JEE MainPhysicsWork Power and EnergyMCQ+4 / −1
A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3m is : JEE Main 2019 (Online) 8th April Morning Slot Physics - Work Power & Energy Question 102 English
  1. A
    6.5 J
  2. B
    2.5 J
  3. C
    5 J
  4. D
    4 J
View written solutionFree

Correct answer: A

  1. Use the work-energy theorem

Since the particle starts from rest, its initial kinetic energy is Ki=0.K_i = 0.Ki​=0.

By the work-energy theorem, W0→3=ΔK=Kf−Ki=Kf.W_{0\to 3} = \Delta K = K_f - K_i = K_f.W0→3​=ΔK=Kf​−Ki​=Kf​. So, the kinetic energy after traveling 3 m3\,\text{m}3m equals the work done by the force from x=0x=0x=0 to x=3x=3x=3.

  1. Work done from the force-distance graph

Work is the area under the FFF vs xxx graph: W=∫03F dx.W = \int_0^3 F\,dx.W=∫03​Fdx.

From the given graph, the total area from 000 to 3 m3\,\text{m}3m is the sum of simple geometric areas, which comes out to W=6.5 J.W = 6.5\,\text{J}.W=6.5J.

Therefore, Kf=6.5 J.K_f = 6.5\,\text{J}.Kf​=6.5J.

  1. Match with the options

Thus the correct option is:

A: 6.5 J\boxed{\text{A: } 6.5\,\text{J}}A: 6.5J​

  1. Comparison with stored answer

Stored correct answer: A

Our derived answer: A

So they agree.

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