Review question

# Can we show the centre of mass moves in a straight line? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6491

## Question

Three particles $A, B$ and $C$, each of mass $m$, are moving in a plane such that at time $t$ their position vectors with respect to the origin $O$ are \begin{align*} (2t+1)\mathbf{i}&+(2t+3)\mathbf{j} \\ (10-t)\mathbf{i}&+(12-t)\mathbf{j} \\ (3t^2-4t+1)\mathbf{i}&+ (-3t^2+2t)\mathbf{j} \end{align*}

respectively.

1. Show that the centre of mass of these three particles moves in a straight line and find the Cartesian equation of this line. Find also the value of $t$ for which the centre of mass is instantaneously at rest.

2. Verify that the particles $A$ and $B$ are both moving along the straight line with equation $y=x+2$ and that they collide when $t = 3$.