Science Dudes: Graphs

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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1PXLupMjj1xnKdrNOSvai0RTCROKmFgrNgGypeBqDvt7YFAqEZ_a1SpSEOlX9VBC_EntLXYSqf1V0mfqMvnKNqLuzRi0nh3-7z4rjGAhaonSy21DxfLh5cTFvBeXMsIbLHF3y0apOoKI/s1600/Photo+Guide+To+Italy+iPhone+Facebook+Post.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Velocity vs Time Graph For Freely Falling object" border="0" data-original-height="789" data-original-width="940" height="268" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1PXLupMjj1xnKdrNOSvai0RTCROKmFgrNgGypeBqDvt7YFAqEZ_a1SpSEOlX9VBC_EntLXYSqf1V0mfqMvnKNqLuzRi0nh3-7z4rjGAhaonSy21DxfLh5cTFvBeXMsIbLHF3y0apOoKI/s320/Photo+Guide+To+Italy+iPhone+Facebook+Post.png" title="Velocity vs Time Graph For Freely Falling object" width="320" /></a></div>
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In free fall, we assume that there's <b>no air resistance.</b> </div>
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<b>The velocity vs time graph for freely falling object is a straight line passing through origin with positive gradient</b>. But why? Before drawing any graphs, you must consider what the equation that relates the parameters in question is. In our case, the equation is <span style="background-color: black;"> </span><span style="background-color: #444444;"><span style="color: white;">v = u + a . t </span></span>, where v = final velocity, u = initial velocity, a = acceleration due to gravity, and t = time.<br />
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But, as we do not supply any initial velocity to the object, u = 0. So the equation becomes <span style="background-color: black;"><span style="color: white;"> v = a . t </span></span><br />
And since a = acceleration due to gravity, it's value is 9.81ms<sup>-2</sup><br />
Therefore, our final equation becomes <span style="background-color: black;"><span style="color: white;"> v = 9.81 * t </span></span><br />
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This equation can be compared with <span style="background-color: black;"><span style="color: white;"> y = mx + c </span></span> where, c = 0. Now m = 9.81, which must be the gradient of the graph.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-kVfKJmGg7YR0DKC3BgVfJ6v0uoLXEVj99Eml3hAXsofITA6oNWaE2jbTSDI3Xu-EmE-uRbT-trYrMzJhulx5JLabywF49VhNPhWY-GarXK29WxUK9Kio77rg-mV-o3Zwa-NhvdfCTnY/s1600/velocity+vs+time.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Velocity vs Time Graph Free Fall" border="0" data-original-height="591" data-original-width="866" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-kVfKJmGg7YR0DKC3BgVfJ6v0uoLXEVj99Eml3hAXsofITA6oNWaE2jbTSDI3Xu-EmE-uRbT-trYrMzJhulx5JLabywF49VhNPhWY-GarXK29WxUK9Kio77rg-mV-o3Zwa-NhvdfCTnY/s320/velocity+vs+time.png" title="Velocity vs Time Graph Free Fall" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Velocity vs Time Graph For Free Fall</td></tr>
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<br />Hence, <b>velocity vs time graph for free fall is a straight line</b> with following properties:<br />
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<li><b>Passes through origin</b>. Why? Because if you compare <span style="background-color: black;"><span style="color: white;"> v = 9.81 * t </span></span> with <span style="background-color: black;"><span style="color: white;"> y = mx + c </span></span>, you'll find that c = 0, which is the y-intercept. If a line has y-intercept of 0, it must go through origin.</li>
<li><b>Has a gradient of 9.81</b>, Why? Again if you compare <span style="background-color: black;"><span style="color: white;"> v = 9.81 * t </span></span> with <span style="background-color: black;"><span style="color: white;"> y = mx + c </span></span>, you'll find that m has a value of 9.81, which is the slope of a straight line. </li>
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Velocity vs Time Graph For Freely Falling Object

In free fall, we assume that there's no air resistance. The velocity vs time graph for freely falling object is a straight line...