teaching:topics:calculus:introduction
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teaching:topics:calculus:introduction [2022/08/30 17:35] simon [Motion] |
teaching:topics:calculus:introduction [2022/08/30 17:37] (current) simon [Motion] |
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| but then how do we find the speed at some instant, when it might be continuously changing? In that instant | but then how do we find the speed at some instant, when it might be continuously changing? In that instant | ||
| - | \(\small0\)m was travelled during \(\small0\)s but we cannot just do \(\small0\div0\), it will not give us a sensible answer. | + | \(\small0\,\)m was travelled during \(\small0\,\)s but we cannot just do \(\small0\div0\), it will not give us a sensible answer. |
| Instead we could consider the **rate of change of position** (over time!), or we could consider a graph we draw with position (that is distance from some fixed place) on the vertical axis and time (since some fixed start time) on the horizontal axis. Then we see that speed is the same as the //slope// of a line on this graph --- the `\ tt{rise}\ \ ` is the same as //change in position//, which is the //distance travelled// | Instead we could consider the **rate of change of position** (over time!), or we could consider a graph we draw with position (that is distance from some fixed place) on the vertical axis and time (since some fixed start time) on the horizontal axis. Then we see that speed is the same as the //slope// of a line on this graph --- the `\ tt{rise}\ \ ` is the same as //change in position//, which is the //distance travelled// | ||
| and the `\ tt{run}\ \ ` is the //time taken// for that to happen. | and the `\ tt{run}\ \ ` is the //time taken// for that to happen. | ||
teaching/topics/calculus/introduction.txt ยท Last modified: 2022/08/30 17:37 by simon
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