Question

At time t = 0 particle starts moving along the x-axis . if Its kinetic energy increases uniformly with time t, the net force acting on it must be proportional to ? [AIEEE 2011]

(a) √t
(b) constant
(c) t
(d) 1/√t​

Answer 1

Answer:

since the kinetic energy increases uniformly hence rate of change of kinetic energy is constant

so does the power so you can write f.v=k

Answer 2

Answer :

Given that, Kinetic energy of moving particle increases uniformly with time t$.$

So we can say that,

• KE ∝ t

We know that, KE = 1/2 mv²

➙ 1/2 mv² ∝ t

➙ v² ∝ t

[∵ mass doesn't vary with time]

➙ v ∝ √t

Differentiating both sides wrt t, we get

➙ dv/dt = d(√t)/dt

➙ a ∝ 1/√t

➙ a = k/√t _____ (I)

Where k is a proportionality constant.

★ As per newton's 2nd law of motion,

➠ F = ma

From equation (I),

➠ F = mk/√t

➠ F ∝ 1/√t (mk = constant)

∴ (D) is the correct answer.

Cheers!