The intersecting lines are said to define a plane, which I take to mean a plane hovering parallel over the road plane. Now 2 and 3 also meet, but if they're meetings intersect on the same plane, doesn't that mean they all met at the same time?

I'll have another look.

And my god that was a quick reply. Many thanks.

Yes. But not only that. They themselves intersect too.

>
>The intersecting lines are said to define a plane, which I
>take to mean a plane hovering parallel over the road plane.

It's defintely not parallel to the plane of the roads. Each of the graphs intersects its corresponding road at time 0. So are the planes.

>Now 2 and 3 also meet, but if they're meetings intersect on
>the same plane, doesn't that mean they all met at the same
>time?

No, why?

>I'll have another look.

A good idea.

>And my god that was a quick reply. Many thanks.

You were lucky.

Then I must be seeing this entirely incorrectly. I'm thinking of first one 2d graph that represents speed, y vs t (time). Uniform motion means a line that has no slope, right? So now I'm thinking of myself standing on the road plane. Off in the corner is another axis going up for time and along one horizon are the four mof i lines for uniform motion going straight up parallel with the time axis. How from here can they intersect without having a slope and representing something other than one particular speed?

>>The intersecting lines are said to define a plane, which I
>>take to mean a plane hovering parallel over the road plane.
>
>It's defintely not parallel to the plane of the roads. Each
>of the graphs intersects its corresponding road at time 0.
>So are the planes.

Uh, ok, I must 100% not understand. There's an x and y graph that represents the location of the people. Perpendicular to that is a graph of their uniform speed. The speed graphs start at time 0, don't they? So everyone is walking, the x and y readout displays are spinning and the speed graphs are moving up and at some point two people meet. So we have a dot on the xy graph and then above their heads is a point that corresponds to their time, an xyt coordinate dot. Where is this intersection at time 0?

Many thanks.

The time axis is perpendicular to that plane. When a fellow moves at a constant speed along a straight line, the graph of his motion is a line in space that is orthogonally projected onto the road of motion.

There is no need to draw x- and y- axes in the plane a. Any pair will do. But, yes, I think of the plane as an xy-plane with the t-axis sticking out.