exercise:Cce54a0398: Difference between revisions
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The velocity <math>v</math> of a freely falling body depends on the distance | |||
<math>s</math> that it has fallen according to the equation <math>v = \sqrt{2gs}</math>, | The velocity <math>v</math> of a freely falling body depends on the distance <math>s</math> that it has fallen according to the equation <math>v = \sqrt{2gs}</math>, | ||
where <math>g</math> is the constant gravitational acceleration. | where <math>g</math> is the constant gravitational acceleration. | ||
<ul style{{=}}"list-style-type:lower-alpha" | |||
<li | <ul style{{=}}"list-style-type:lower-alpha"> | ||
Using an <math>s</math>-axis and a <math>v</math>-axis, plot the dependent variable <math>v</math> | <li id="ex1.3.7a">Using an <math>s</math>-axis and a <math>v</math>-axis, plot the dependent variable <math>v</math> as a function of the independent variable <math>s</math>.</li> | ||
as a function of the independent variable <math>s</math>.</li> | <li id="ex1.3.7b">If <math>s</math> depends on the time <math>t</math> according to the equation <math>s=\frac12gt^2</math>, how does <math>v</math> depend on <math>t</math>?</li> | ||
<li | |||
If <math>s</math> depends on the time <math>t</math> according to the equation | |||
<math>s=\frac12gt^2</math>, how does <math>v</math> depend on <math>t</math>?</li> | |||
</ul> | </ul> | ||
Note that the variable <math>v</math> | |||
which depends on <math>s</math>, is not the same function as the | Note that the variable <math>v</math>, which depends on <math>s</math>, is not the same function as the variable <math>v</math>, which depends on <math>t</math>. Without knowing which is referred to, the meaning of the value of <math>v</math> at 2 is ambiguous. | ||
variable <math>v</math> | |||
Without knowing which is referred to, the meaning of the value of | |||
<math>v</math> at 2 is ambiguous. | |||
Latest revision as of 22:54, 22 November 2024
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[/math]
The velocity [math]v[/math] of a freely falling body depends on the distance [math]s[/math] that it has fallen according to the equation [math]v = \sqrt{2gs}[/math], where [math]g[/math] is the constant gravitational acceleration.
- Using an [math]s[/math]-axis and a [math]v[/math]-axis, plot the dependent variable [math]v[/math] as a function of the independent variable [math]s[/math].
- If [math]s[/math] depends on the time [math]t[/math] according to the equation [math]s=\frac12gt^2[/math], how does [math]v[/math] depend on [math]t[/math]?
Note that the variable [math]v[/math], which depends on [math]s[/math], is not the same function as the variable [math]v[/math], which depends on [math]t[/math]. Without knowing which is referred to, the meaning of the value of [math]v[/math] at 2 is ambiguous.