Question

5.
the momentum p (in kg m/s) of a particle is varying with time t (in s) as p = 2 +3t^2. The force acting on the particle
at t = 3 s will be
(1) 18 N
(2) 54 N
(3) 9N
(4) 15 N
I know the answer is 18 N, but I don't know how it is. please explain it. I am weak in math and physics. please answer me​

Answer 1

$\huge\mathfrak\red{Answer}$

WHAT IS LINEAR

MOMENTUM

Just think which require more force in order to stop completely A bullet or a Truck. ACC to me and scientists both require equal magnitude of force in most cases.

So in order to relate the entirely two different things (velocity,mass) Scientists found a way namely momentum which is basically the product of mass with velocity.

Further Development

After that a Scientist come in to play namely Newton which gave some law related to force. And say that rate of change in linear momentum is equal to force applied.

$p = 2 + 3 {t}^{2} \\ differentiate \: the \: equation \\ \\ \frac{dp}{dt} = 0 + (2)(3)t \\ \\ \frac{dp}{dt} = force \\ \\ force = 6t \\ put \: t = 3sec \\ \\ force = 18newton$