The linear momentum of a particle varies with time t as `p= a +bt + ct^(2)`. Then, whichh of the following is correct?

Options

A. Velocity of particle is inversely proportional to time
B. Displacement of the particle is independent of time
C. Forces varies with time in a quadratic manner
D. Force is independent linearly on time

Answer

D

Explanation

Given, `p=a +bt+ct^(2)`
Differentiating with respect to t(time), we get,
`(dp/dt) = 0+b + 2ct`
From Newton's second law of motion, `Falpha(dp)/(dt)` ltbr. `rArr alpha t`, force is dependent linearly on time.