# Instantaneous Speed Tutorial - what is it, and how to calculate it

NinetyEast
Published at : 09 Nov 2020
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Check out the associated tutorial here: http://www.ninetyeast.net/physics/grade-11-12-ib-a-levels/speed/instantaneous-speed
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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.

In the last couple of videos (https://youtu.be/p1D1WIqbJtY and https://youtu.be/l93-BkAJ3UY) we have been looking at how to calculate the average speed of an object when its journey is represented on a distance-time graph. The graphs that we've been looking at have 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.

This 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.

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 the previous videos, 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.

This is the worksheet associated with this video: http://www.slideshare.net/NinetyEast/instantaneous-speed-exercises It has a two worked through examples in the introduction, and five exercises for you to work through in your own time. If you get a different answer, there are worked through calculations for each exercise that you can compare your calculations against.

Would you like the slides for this video so that you can make notes as you follow along? No problems - just grab them here: http://www.slideshare.net/NinetyEast/instantaneous-slides

You can turn the subtitles / captions on and off as you please, using the button in the bottom right hand corner.

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