Question

the momentum p of particle is varying with time t as p=2+3t^2 force acting on particle at t=3s will be

Answer 1

Answer: The force at 3 sec will be 18 N.

Explanation:

Given that,

Time t = 3 sec

Momentum $p= 2+3t^{2}$

We know that,

The force is the rate of change of momentum.

The force is

$F = \dfrac{dp}{dt}$

$F = \dfrac{d}{dt}(2+3t^{2})$

$F = 6t$

Now, at t = 3s

$F = 6\times3$

$F = 18 N$

Hence, the force at 3 sec will be 18 N.

Answer 2

"Answer: Force acting on particle = 18 Newton

Given:

Momentum “p” changes with time t

Solution:

We know that, according to Newton's second law, rate of change of momentum is directly equal to the "resultant force" acting on the "body".

$Force\quad =\quad \frac { dp }{ dt }$

Given, $p\quad =\quad 2\quad +\quad 3{ t }^{ 2 }$

Differentiating with respect to t,

$\frac { dp }{ dt } \quad =\quad 0\quad +\quad \left( 2\quad \times \quad 3t \right) \quad =\quad 6t$

Given, t = 3secs

$Force\quad =\quad 6\quad \times \quad 3\quad =\quad 18\quad Newton$"