This is a simple physics tutorial aimed at high school students in grade 11 and 12 (international baccalaureate / HSC / A-levels) explaining what instantaneous speed is and how to calculate it from a distance-time graph. There is both a video and written tutorial.
See below for some useful associated resources.
What is instantaneous speed?
In earlier material, we learned how to calculate the average speed of an object when its journey is represented on a distance-time graph. The graphs covered so far illustrated journeys where the object is travelling at a constant rate.
But objects and people do not travel at a constant speed. Instead, we actually vary our speed during a journey. This may be because we have to slow down to let someone cross the road, or stop at a traffic light. But it's also because it's simply not possible for a car to go from rest (e.g. parked in the garage) to a normal travelling speed (e.g. 50+ km/hr or 30+ mi/hr) right away. Instead you need to build up to that speed.
The above video reviews the distance-time graph for a person going from standing to walking i.e. a curved distance-time graph. In an exam or an assignment, you may be asked to calculate the instantaneous speed of an object on a similar graph. The 'instantaneous speed' of an object just refers to its speed at a particular point in time.
How do I calculate the instantaneous speed of an object from a distance-time graph?
To do this, you need to simply draw a tangent at the point in the curved graph. Then you calculate the speed by calculating the gradient of the tangent. NB: this is only the case if distance is plotted on the y-axis, and time is plotted on the x-axis. If the graph is plotted with the axes are swapped around, you need to calculate the inverse of the gradient (see related worksheet).
Although we've already covered how to calculate the gradient of a line in previous tutorials, this is reviewed again, as some people may have trouble calculating the change in time when the line does not intersect with the origin of the graph.
Below is the worksheet associated with this video. It has a two worked through examples in the introduction, and three exercises (with worked through calculations for each exercise) for you to work through in your own time. You can download the document here: