(a) Show that the velocity of the centre of mass of a moving isolated system remains constant.

Explanation

To show that the velocity of the center of mass of a moving isolated system remains constant, we can follow these steps:

### Step 1: Define an Isolated System
An isolated system is defined as a system where no external forces are acting on it. This means that the net external force acting on the system is zero.

### Step 2: Use the Equation of Motion
According to Newton's second law, the net external force (\( F_{\text{net}} \)) acting on a system is equal to the mass (\( m \)) of the system multiplied by the acceleration (\( a \)) of the center of mass:
\[
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