Question

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 -

(1) 2.5 J  (2) 6.5 J  (3) 4 J  (4) 5 J

Answer 1

Correct option is (2) 6.5 J

According to Work Energy Theorem,

Work done by force on the particle = Change in KE

Work done = Area under F − x graph

= ∫F.dx

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

= 6.5 J

W = KE_final − KE_initial = 6.5 J

KE_initial = 0

∴ KE_final = 6.5 J

Answer 2

Correct option (2) 6.5 J

Explanation:

1/2  mV² = 4 + 2 + 0.5 = 6.5 J