# 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 :Option 1)$6.5 J$  Option 2)$4 J$Option 3)$2.5 J$  Option 4)$5 J$

Answers (1)

Work Energy theorem

$W=k_{f}-k_{i}$

$k_{i}=0$

$k_{f}=w$

Now work is Area of F vs distance curve.

$k_{f}=(2\times 2)+(\frac{1}{2}\times (2+3)\times 1)$

$k_{f}=6.5 J$

Option 1)

$6.5 J$

Option 2)

$4 J$

Option 3)

$2.5 J$

Option 4)

$5 J$

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