Unit 7B

Integrals Part 2

Lesson 2: Displacement, Velocity, and Acceleration

Watch the video Displacement, Velocity, and Acceleration for an example of how these concepts are linked together. Note the notation for the position function is denoted by «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»d«/mi»«mfenced»«mi»t«/mi»«/mfenced»«/math» in the video instead of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mfenced»«mi»t«/mi»«/mfenced»«/math».

In the video, the terms displacement and distance are used interchangeably. Distance is a term that is used more commonly in mathematics, whereas, displacement is a term that is used in physics. It is important to be aware of the context in which a position function is given to understand if it represents distance or displacement.

For example, in the video, Farmer Greg reached a maximum height of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»196«/mn»«mi mathvariant=¨normal¨» «/mi»«mo»§#160;«/mo»«mi»ft«/mi»«/math» (his maximum height). However, he also started at a height of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»160«/mn»«mo»§#160;«/mo»«mi»ft«/mi»«/math». So, he only flew «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»36«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨» «/mi»«mi»ft«/mi»«/math» higher into the air, but his total vertical distance travelled was «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mn»196«/mn»«mo»§#160;«/mo»«mi»ft«/mi»«mo»§#8722;«/mo»«mn»160«/mn»«mo»§#160;«/mo»«mi»ft«/mi»«/mrow»«/mfenced»«mo»+«/mo»«mn»196«/mn»«mo»§#160;«/mo»«mi»ft«/mi»«mo»=«/mo»«mn»232«/mn»«mo»§#160;«/mo»«mspace width=¨0.125em¨/»«mi»ft«/mi»«/math», and his displacement was actually «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»160«/mn»«mo»§#160;«/mo»«mi»ft«/mi»«/math» since he landed «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»160«/mn»«mo»§#160;«/mo»«mi»ft«/mi»«/math» below where he started. So, be careful to consider context, and even draw a diagram to eliminate any risk of confusion.