# 2 1 b Equations of motion for IB Physics

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We start with a puzzle. Many physics

students have seen the four well-known equations of motion here, but in fact,

since there are five variables, there is also a fifth equation. Do you know what

it is? The solution will be given near the end of the video. Welcome to this

NothingNerdy video on equations of motion. Here is the statement from the IB

physics guide. You should be able to make calculations about uniformly accelerated

motion using the three formulas in the data booklet. Here is a typical multiple

choice question on this topic. You should be able to answer it by the end of the

video. The equations of motion are used for calculations about motion for which

the velocity changes uniformly. This diagram shows a moving object with a

constant acceleration which is represented by the letter a as well as

the final and initial velocities v and u, the other variables in the equations are

displacement s and time taken t. There are five possible equations of motion.

Each one connects four of the quantities which describe uniformly accelerated

motion. Here is the first one which is made by rearranging the definition of

acceleration: v equals u plus a*t. Each equation includes four of the five

variables. Another way of looking at it is that one variable is not included in

the equation. For example v equals u plus a*t includes v, u, a and t, but not s. Another equation of motion is found by equating two formulas for average

velocity. This is the equation which does not include acceleration, a. s equals v

+ u times t over 2. If we now substitute equation 1 into equation 2 we

can make a third equation: s=u*t + half a t squared. Here, v is the variable which is not used. The fourth equation is also found by combining two equations. If you’re interested in how it’s done, pause the video and study this derivation. The resulting equation is v

squared equals u squared plus 2a*s which uses all of the variables except for t. There is a very useful method to avoid mistakes when making calculations which follows the acronym IF SEA UP: information – formula – substitute – evaluate – answer – unit – precision. Let’s apply the IF SEA UP method to a question: A plane lands and its velocity changes from 100 to 20 meters per second over

a distance of 720 meters. What is its average acceleration? So the information

we have is v u and s which is three variables, so we know we can find any of

the others. We need a. The formula using these variables is v squared equals u

squared plus 2 a*s. We rearrange it to find a and then we substitute in the

numbers and finally we arrive at 6.7 meters per second squared.

The precision should be two significant figures which is the same as the least

precise figure which is 20 meters per second, so we write that the acceleration

is six point seven meters per second squared in the opposite direction to the

motion. For this question we have to decide which formula to use so that we know we have the quantities s and t and u and we want to find a and therefore s

equals ut plus a half at squared is the formula we’re going to use. We substitute

into that the numbers that we know. We rearrange it and that will give us this

calculation here. 100 divided by 6.5 and the answer is 16 meters per second squared Here is the answer to the puzzle we asked at the beginning: Most textbooks mentione four equations and it’s true that we can

calculate anything using these, but there is a fifth one which is the equation

which omits the initial velocity u. it is found using the same method we

used to prove s equals ut plus a half a*t squared The result is very similar: s

equals vt minus a half a*t squared.