Question

the linear momentum of a particle as a function of time is given by P is equals to a + b t where A and B are positive constants what is the force acting on the particle​

Answer 1

Answer:

Given:

Linear momentum is given as :

P = a+ bt

To find:

Force acting on the particle.

Concept:

Force is actually the rate of change of momentum. Mathematically :

$\boxed{force = \dfrac{d(p)}{dt}}$

Calculation:

$p = a + bt$

$force = \dfrac{d(p)}{dt}$

$= > force = \dfrac{d(a + bt)}{dt}$

$= > force = 0 + b \: = b$

So final answer :

$\boxed{force = b \: units}$

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

$\small{\underline{\blue{\sf{Given :}}}}$

$\rule{200}{1}$

• p = a + bt

$\small{\underline{\green{\sf{Solution :}}}}$

As we know that :

$\large \star {\boxed{\sf{F \: = \: \dfrac{dp}{dt}}}} \\ \\ \small{\pink{\sf{Put \: Value \: of \: p}}} \\ \\ \\ : \implies {\sf{F \: = \: \dfrac{d(a \: + \: bt}{dt}}} \\ \\ : \implies {\sf{F \: = \: (0 \: + \: b)}} \\ \\ \small{\orange{\sf{By \: differentiating \: with \: dt}}} \\ \\ : \implies{\sf{F \: = \: b }} \\ \\ \\ {\boxed{\sf{F\: = \: b \: units}}}$