Question

27. The linear momentum of a particle is P=1/(1-t). The
force on the particle at t=2s is
(a) 1
(b) 2
(c) 1.5
(d) 3​

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.

$p = \frac{1}{(1 - t)} \\ \\ differentiate \: the \: equation \: with \: respect \\ to \: time \\ \\ \frac{dp}{dt} = \frac{d {(1 - t)}^{ - 1} }{dt} \\ \\ \frac{dp}{dt} = force \: applied \\ \\ f = ( - 1) {(1 - t)}^{ - 2} ( - 1) \\ f = {(1 - t)}^{ - 2} \\ put \: t = 2 \\ \\ f = \frac{1}{ {(1 - t)}^{2} } \\ f = \frac{1}{ {(1 - 2)}^{2} } \\ f = \frac{1}{ {( - 1)}^{2} } \\ \\ force \: is \: equal \: to \: 1 \: newton$