Question

show that in the absence of external force the c.m moves with constant velocity ?​

Answer 1

To show:

In absence of a external force the centre of mass moves with constant velocity.

Calculation:

We shall use calculus to prove the above statement.

Let's consider that a point object is placed on a road and was moving with an initial velocity u , and does not experience any force.

$\therefore \: F = 0$

$= > \: m \times a = 0$

$= > \: a = 0$

$= > \: \dfrac{dv}{dt} = 0$

$= > \: dv = 0 \times dt$

Integrating on both sides:

$= > \: \displaystyle \int_{u}^{v} dv = \int_{0}^{t} \: 0 \times dt$

$= > \: v - u= 0$

$= > \: v = u$

So, final velocity is equal to the initial velocity.

Hence the object moves with constant velocity.