Thinking about journeys

The journey described by our velocity-time graph was along a straight road.

For each of the situations below, can you sketch a speed-time graph and a velocity-time graph?

  • Do the graphs look the same?

  • Are they both possible to draw?

Situation one

You walk straight to school travelling at a constant speed of \(\quantity{0.5}{m\,s^{-1}}\).

Distance between home and school is 150 metres.
The speed time graph is a constant line with the speed equal to 0.5.
The velocity time graph is a constant line with the velocity equal to 0.5.

The graphs look identical here as we have measured our positive velocity in the direction of ‘home to school’. How would the graphs differ if we measured positive velocity in the opposite direction?

How many dimensions is our journey taking place in?

Situation two

You walk straight along the road from home to school and at the end of the first road you take a \(90^{\circ}\) turn left. You travel at a constant speed of \(\quantity{0.5}{m\,s^{-1}}\).

walk 100 metres straight then turn left and walk 50 metres.

At faster speeds we would expect to slow down when we approach and turn a corner. Here we are making the assumption that the constant speed of \(\quantity{0.5}{m\,s^{-1}}\) is maintained.

The speed time graph is a constant line with the speed equal to 0.5.

While the speed-time graph is easy to draw, the velocity-time graph should have made you stop and think. What happens when you turn the corner?

The velcity time graph up to 200 seconds is a constant line with the speed equal to 0.5 .

In what direction are we measuring velocity?

Can you graph anything for \(t>200\)? Is it meaningful?

We have seen that journeys in one dimension can easily be represented on displacement-time and velocity-time graphs. However it is not possible to represent journeys in two dimensions in the same way. In order to work with journeys in two (or more) dimensions we use vectors.