Question

Derive the equation for (i) position vector (ii) velocity (iii) acceleration of
centre of mass of a two particle system.

Answer 1

Answer:

Calculating the Velocity Vector

The position function of a particle is →r(t)=2.0t2^i+(2.0+3.0t)^j+5.0t^km.

Instead of differentiating velocity to find acceleration, integrate acceleration to find velocity. This gives us the velocity-time equation. If we assume acceleration is constant, we get the so-called first equation of motion [1].

...

calculus derivations.

v = v0 + at [1]

=

v2 = v02 + 2a(s − s0) [3]

Acceleration of the Center of Mass

The net (external) force on a system of particles equals the mass of the system times the acceleration of the system's center of mass. ... The system behaves as if all of its mass were located at the system's center of mass