Question

a particle of mass 15 kg is moving with 5m/s along a straight line and a force of 30n is acting on it opposite to the direction of velocity what is the work done in joules by the force during the third second of motion of the particle

Answer 1

workdone by the force during the 3rd second of motion of the particle is 0J

A particle of mass , m = 15kg is moving with v = 5m/s along a straight line and a force , F = 30 N is acting on it opposite to the direction of velocity.

we have to find the workdone in joules by the force during the 3rd second of motion of the particle.

now using formula, F = ma

⇒-30 = 15a [ negative sign indicates force is acting opposite direction of its motion]

⇒ a = -2m/s²

at t sec, velocity of particle becomes zero.

using formula, v = u + at

⇒0 = 5 - 2t

⇒t = 2.5 sec

displacement of particle in 2.5 sec , s₁ = ut + 1/2 at²

= 5 × 2.5 - 1/2 × 2 × (2.5)²

= 12.5 - 6.25

= 6.25 m

so after 2.5 sec particle moves opposite direction of its initial motion.

now displacement of particle from 2.5 sec to 3.0 sec, s₂ = 1/2 × 2 × (0.5)²

= 0.25 (opposite direction of its initial motion)

now total displacement of particle, s = s₁ + s₂

= 6.25 - 0.25 = 6m

so, workdone by the force in 3sec = force × velocity = 30N × 6m = 180 J

again, displacement of particle in 2sec = 5m/s × 2sec - 1/2 × 2m/s² × (2s)²

= 10 - 4 = 6m

so, workdone by the force in 2sec = 30N × 6m = 180

therefore workdone by the the force during 3rd second = workdone by the force in 3s - workdone by the force in 2s

= 180J - 180 J = 0