Equations of Motion

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In the previous lesson we looks at graphing motion.
If motion can be graphed and there are certain trends, then there are mathematical equation that describe that trend.

In this lesson we examine these mathematical equations.
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There are relationships between each of the variables involved in kinematics and these mathematical relationships are modelled in what are know as the kinematic equations, or equations of motion. 
Picture
though the two in red are less commonly used
​Theory
Watch the video which covers the 5 forms of kinematic equations and how they are derived.
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How to Solve physics Problems
Before we look at a sample problem, there is a useful technique to use consistently when doing calculation type problems and it requires you to be RUDE.
​Read Understand Data Equation.
Watch the video as I explain
Sample Problem
We are now ready to try a sample problem
Below is a sample problem with a video that explain how to solve it. It is suggested you try the problem beforehand, as this actually aids understanding, even if you are unsure if you are correct.
Picture

Here are some more problems for you to try. Answers are provided. 

  1. A car travels 20 km at 40 kmh-1. What speed should the car at the next 20 km to have an average speed of 60 kmh-1 for the whole journey?  (120 kmh-1) 
  2. A car leaves home at 8 am and travels at 60 kmh-1. Another car leaves the same home at 8:30 am and  was at 80 kmh-1. When and where will the second car overtake the first car? (10am, 120km) 
  3. An aircraft needs to reach a speed of 80 ms-1 before it can take off. If it accelerates at 3  ms-2 , calculate the length of the run by used. (1070m) 
  4. An object moving with a constant acceleration can certainly slow down. But can an object ever come to a permanent halt if it’s acceleration truly remains constant? Explain. 
  5. A car with its brakes full on decelerates at 4  ms-2. If the car is moving uniformly at 20  ms-1 when a cow crosses 60 m in front of it, and if it takes a car six seconds to come to rest, calculate how long it took the driver to apply the brakes. Does it hit the cow? (1 sec, yes they hit the cow)
GOING FURTHER

Determing the equations of motion using graphical Analysis or algebraically are not the only way to derive them.
A more powerful way is too use calculus



​In this video, using both differential and integral calculus, I show how the equations of motion are derived.

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