Question

the linear momentum of a particle as a function of time is given by p=a+bt ,where a and b are positive constants what is the force acting on the particle

Answer 1

Force is rate of change of momentum.

If p = a + bt
Then
dp/dt = 0 + b

Therefore force acting on it is “b”

Answer 2

Given:

The linear momentum of a particle is a function of time $p=a+bt$.

To Find:

Force acting on the particle.

Solution:

From Newton's second law of motion, we know that the force acting on a body is directly proportional to the rate of change of its linear momentum.

So we can write, Force $F=\frac{dp}{dt}$

In this problem, we are given the linear momentum of the particle as a function of time, $p=a+bt$, where $a$ and $b$ are positive constants

∴  $F=\frac{d}{dt} (a+bt)$

⇒ $F=b$ units.

Hence the force on the particle is equal to $b$ units.