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phys: clarify change of area on graphs

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eggy 2020-10-02 13:14:13 -04:00
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@ -280,13 +280,13 @@ A **velocity-time graph** is similar to a position-time graph but replaces the p
On a velocity-time graph, the slope represents that object's acceleration. If the slope is not linear, the object is not accelerating uniformly (accelerating at a constant rate). On a velocity-time graph, the slope represents that object's acceleration. If the slope is not linear, the object is not accelerating uniformly (accelerating at a constant rate).
The area below a velocity-time graph at a given time is equal to the displacement (change in position) at that time, since $ms^{-1}×s=m$. When finding the displacement of an object when it is accelerating, breaking up the graph into a rectangle and a triangle then adding their areas will give the displacement. The area below a velocity-time graph at a given time is equal to the displacement (change in position, $\Delta d$) at that time, since $ms^{-1}×s=m$. When finding the displacement of an object when it is accelerating, breaking up the graph into a rectangle and a triangle then adding their areas will give the displacement.
<img src="/resources/images/velocity-time-displacement.png" width=700>(Source: Kognity)</img> <img src="/resources/images/velocity-time-displacement.png" width=700>(Source: Kognity)</img>
An **acceleration-time graph** is similar to a velocity-time graph but replaces the velocity on the vertical axis with an object's acceleration instead. An **acceleration-time graph** is similar to a velocity-time graph but replaces the velocity on the vertical axis with an object's acceleration instead.
The area below an acceleration-time graph at a given time is equal to the change in velocity at that time. The area below an acceleration-time graph at a given time is equal to the change in velocity ($\Delta v$) at that time.
!!! note !!! note
If there is any instantaneous jump on a position-, velocity-, or acceleration-time graph (which is impossible in reality but may be used to simplify matters), a dashed line must be used to connect the two sides to ensure that the line remains a function. If there is any instantaneous jump on a position-, velocity-, or acceleration-time graph (which is impossible in reality but may be used to simplify matters), a dashed line must be used to connect the two sides to ensure that the line remains a function.