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 3 m is:

This question was previously asked in

JEE Mains Previous Paper 1 (Held On: 08 Apr 2019 Shift 1)

Option 3 : 6.5 J

JEE Mains Previous Paper 1 (Held On: 12 Apr 2019 Shift 2)

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90 Questions
360 Marks
180 Mins

**Concept: **

Work energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.

**Calculation:**

According to work energy theorem:

Work done by force on the particle = Change in kinetic energy

Work done = Area under F-x graph

Work done = Force × Distance

\(\text{W}=\left( \frac{1}{2}\times \left( 3+2 \right)\times \left( 3-2 \right) \right)+2\times 2\)

W = 2.5 + 4

W = 6.5 J

Now, we need to use work energy theorem.

W = KE_{final }– KE_{initial}

W = 6.5 – 0

W = 6.5 J