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 :
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 :
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By the work-energy theorem, the kinetic energy gained equals the area under the F-x graph from 0 to 3 m (the particle starts from rest).
Updated On: Nov 5, 2026
- 6.5 J
- 2.5 J
- 5 J
- 4 J
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The Correct Option is A
Solution and Explanation
Graph: F = 2 N from x = 0 to 2 m; F rises linearly from 2 N to 3 N from x = 2 m to 3 m.
Work from 0 to 2 m: rectangle \(= 2\times2 = 4\) J.
Work from 2 m to 3 m: trapezium \(= \dfrac{2+3}{2}\times1 = 2.5\) J.
Total work \(W = 4+2.5 = 6.5\) J.
Work-energy theorem: \(K_f - K_i = W\) and \(K_i = 0\), so \(K_f = 6.5\) J.
Answer: (1) 6.5 J
Work from 0 to 2 m: rectangle \(= 2\times2 = 4\) J.
Work from 2 m to 3 m: trapezium \(= \dfrac{2+3}{2}\times1 = 2.5\) J.
Total work \(W = 4+2.5 = 6.5\) J.
Work-energy theorem: \(K_f - K_i = W\) and \(K_i = 0\), so \(K_f = 6.5\) J.
Answer: (1) 6.5 J
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