### Introducing Calculus

Problem requiring decisions

The journey described by our graphs was along a straight road. This is a very simplistic and unlikely journey in the real world.

For each of the situations below, can you sketch a distance-time graph and a displacement-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 $\quantity{0.5}{m\,s^{-1}}$.

### 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 $\quantity{0.5}{m\,s^{-1}}$.

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.

Representing a simple journey in two dimensions can become complicated when we think about displacement, rather than distance travelled. Does the same happen with speed and velocity? These questions are considered in Speed vs velocity.