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

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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.

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.

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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[kingcloud]

Hi I hope I'm not too late, I have a question about the length of the tangent line drawn to the curve. How do you know when to stop extending it? for example, your example at 0:53 and 2:54

[_arlyn]

How do we solve without a graph?
For example, car initially traveled 40m/s that accelerates at 5m/s for 3s.
How would you set up the formula/equation.

[JamesPeach]

Hmm, how do you know where to draw the tangent?

[adosar]

sry if is a nonsense question but why we use derivatives in order to calculate the instantaneous speed instead of arithmetic?

[Magnezium]

Would you mind explaining the formula to me?

Do you always have to draw to solve it?

[amnahussain]

Thank you. This video really helped. :")

[syasya]

hello i really need help catching up with my physics since i missed a week of school.do you mind helping.thanks before