Velocity

Velocity is speed in a direction.

An example is 5 kilometres per hour east.

The speed is 5 kilometres per hour and the direction is east.

Imagine a long, flat, straight road that goes west to east. The road is like a line segment. Imagine a car on the road. Imagine that you are the driver and you have just got in the car, started the engine and are now driving east along the road.

At the beginning of your journey the car is still. It is at 0km/h. You accelerate to 36km/h in the first thirty seconds of the journey with constant acceleration, then you drive at 36km/h east for five minutes and then decelerate to 0km/h with constant deceleration in the last 30 seconds.

Let’s draw a graph of this journey. Time usually goes on the x-axis. The journey is short, only 6 minutes. Let’s plot the time on the x-axis in seconds.

As we are plotting the time is seconds, let’s plot the velocity in metres per second (m/s). 36 km/h is 36000 metres per hour because there are 1000 metres in a kilometre. We want to convert 36000 metres per hour into metres per second. If we divide 36000 by 60 then we will have the number of metres per minute because there are 60 minutes in an hour. This is 600. 600 metres per minute. If we divide this by 60 again then we will have the number of metres per second as there are 60 seconds in a minute. 600 divided by 60 is 10. 36km/h is the same speed as 10m/s.

We know the speed that we are going to plot but we will be plotting velocity which we know is speed in a certain direction. As the road the car is travelling down only goes east or west then we can set one of these as positive and one as negative for our plot. Let’s plot east as positive. If we plot a point at 10m/s then this will mean the car is travelling east at 10m/s. If we plot a point at -10m/s then this will mean a car is travelling west at 10m/s.

Right! Let’s start the plot…Velocity in metres per second in on the y-axis and time in seconds is on the x-axis. As the car is travelling east or is stationary then we only need 0 and positive velocities on the y-axis. The car has stopped its journey after 6 minutes which is 360 seconds so 360 is the largest number we need on the x-axis.

Let’s plot all of the important points on the graph. These are shown in the table below.

And here they are on the plot

Now we can draw straight lines to connect these points. The constant acceleration from 0 to 10m/s in the first 30 seconds is shown by a straight line connecting these points. The car travelling at 10m/s for the next 5 minutes (or 300 seconds) is shown by the straight line connecting the two points at the top of the plot and the constant deceleration to 0m/s is shown by the straight line connecting the last two points.