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 3 m is ______.

Options

• 4 J

• 2.5 J

• 6.5 J

• 5 J

Answer 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 3 m is 6.5 J.

Explanation:

Given: The variation of a particle's force as a function of its distance travelled.

To find: The particle's kinetic energy at x = 3 m. The area under the curve ABC represents the work done by the force on the particle.

ΔW = Area of square ABEO + area of rectangle BDFE + area of triangle BCD

= `(2 xx 2) + (2 xx 1) + (1/2 xx 1 xx 1)`

= 4 + 2 + `1/2 = 6.5` J

According to the work-energy theorem:

K_f - K_i = ΔW = 6.5 J