hey everyone I am Miss who your physics teacher in this video we are going to be learning about linear motion this video Lesson will be covering an introduction to distance and displacement speed and velocity as well as acceleration now first things first what does linear motion mean from this term it's quite obvious but we'll go through the meaning anyway so as you know the term linear means straight line whereas motion refers to movement therefore linear motion specifically refers to movement in a straight line so under the concept of linear motion we will be learning about distance and displacement speed and velocity as well as acceleration now the thing is about distance and displacement as well as speed and velocity you have to understand the concept of scalar and Vector if you have not learned about scalar and Vector please watch my video where I explain the concept of scalar and vector and what the differences are for now let's get into the comparisons of distance and displacement as well as speed and velocity so when it comes to linear motion it's all about the object's moving in a straight line it's possible for the object to change direction but throughout a particular motion the object will be moving in a straight line and this will be seen in the examples in the next few slides so here's a very simple example we have this in 2D and we're first going to look at distance versus displacement so let's say we have a red ball that's going to be traveling from o to R to S so if we were to calculate the distance so when traveling from o to R first it has traveled 10 m and then when traveling to S it has gone backwards but in this case because we're calculating the distance traveled you just need to count how far the object has moved overall so that's why we add another 10 and 8 m as per the diagram this gives us the total distance travel of 28 M so you can see that in this case it doesn't matter which direction that the ball is moving when calculating the total distance traveled we just count what distance it's actually moved just like if you were in a car you would observe the autometer and see how far you've actually moved it doesn't matter which direction you're moving it's just how far you've actually traveled however when we want to calculate displacement let's start from o again now displacement has both magnitude and direction so in this case we're going to express a direction by using positive and negative so when the red ball is moving to R it's moving to the right so we take that value as positive 10 m now when the ball moves to S it's moving to the left so we're going to take that displacement as negative and that's why we have - 10 and then minus 8 so this is how you calculate displacement as you can see when the object moves from o to R and back to O the value kind of cancels itself out because it goes there and comes back and moves backwards again an additional 8 mters and that's why you end up with a displacement of -8 M so this proves mathematically how we get the value of the displacement so now that you understand this let's look at an easier way to calculate displacement all you need to do is is find out where it starts and where it ends and take the displacement from start to end based on the magnitude and direction in this case we can see it starts at o ends up at s so direct from start to finish it's 8 m to the left and that's why a simple way of determining the displacement is just putting it as -8 M based on the start and as well as the direction now let's look at the speed and velocity say in this case when traveling from O2 R to S the time taken in total is 20 seconds let's start first with the speed calculation we already know that the distance traveled in total is 28 M so to calculate the speed all you need to do is take the distance of 28 M divided by 20 seconds and that's how we get 1.4 m/s as the average speed speed of the entire motion when it comes to Velocity we need to take the value of the displacement so we know the displacement is 8 m the total time taken is 20 seconds because that is the total time for the entire motion of this red ball so that's why the velocity is -8 M divided by 20 seconds giving us 0.4 m/s that is the average velocity for the entire motion of the red ball traveling from o to R to S let's look at one more example so again we're going to have the same red ball with the same set up but this time this red ball is traveling from o to R to S and back to O remember that when calculating distance it doesn't matter which direction that the object is traveling in so when traveling from o to R the distance travel is 10 m and then when it goes to S we're going to add another 10 and an eight and then back to always another 8 m this gives us a total distance of 36 M the displacement on the other hand would be positive 10 when it travels to R -10 and another 8 when it moves backwards to S and when it goes back to O we add 8 m again so mathematically when you look at this this gives us a displacement value of zero now let's recall the faster way to determine the displacement all you need to do is look at the start the end and the direction in this case you can see that the start and finish finish are at the same point and that's why this red ball has zero displacement so in spite of all its motion because it started and ended at the same point the displacement is zero so now let's look at speed and velocity starting first with speed if let's say the time taken for the entire motion is 25 seconds we know that the distance traveled is 36 M so so we take the speed as 36 / by 25 and this gives us the average speed of 1.44 m/s for the entire motion for velocity we're going to take the value of displacement but we know that the displacement is zero so it doesn't matter what the total time is if the displacement is zero therefore the velocity is also zero it's as if the object never moved even though it did but that's a thing when it comes to Vector quantities for displacement we look at the start and finish and because velocity depends on the value of displacement that's why we also look at start and finish in this case both values are zero let's look at one more example to help you cement your understanding of distance displacement speed and velocity in this case this is not a flat line we have a situation here where we've got different dire directions so let's say someone is going to start walking from home to a shop that's 3 km away then from the shop the person takes a right angle turn and travels 4 kilomet to go to school so if you want to calculate the distance all you need to do is add the two values up together and that's how we get the total distance traveled at 7 kilm let's say this person took 1 hour to travel so therefore for the average speed in total would be 7 kilm divided by 1 hour giving us the average speed value of 7 kilm per hour so in this case how are we going to calculate the displacement we can't use positive and negative because the directions here are different right so let's recall what we've learned earlier to determine the displacement all you need to do is find the starting point the ending point and the direction between those two points so in this case you can see this is a very simple example the 3km and 4km lines form a right angle so the displacement is directly from home to school like so to determine the value because this is a right angle triangle you just need to use Pythagoras Theorem and that's how we get the value of the displacement at 5 kilom now remember that displacement is a vector quantity so which means that we also need to determine the direction of the displacement how do we determine the direction because we're using a right angle triangle to solve this problem all we need to do is take the angle between that resultant displacement from one of the lines in this case let's take it from the 3 kilm line so to determine the angle we're just going to use trigonometry which in this case we can use tangent so we get tangent theta equals to 4 over3 and that's how we get the value of the angle at 53.1 De to calculate the velocity just like earlier all you need to do is take the value of the displacement divided by time so in this example the time taken is 1 hour which means that the velocity is just 5 km ided 1 hour giving us the average velocity of 5 km per hour the direction of the Velocity is exactly the same as the direction of the displacement so now that we know what distance displacement speed and velocity are let's go through the concept of acceleration now the definition of acceleration is the rate of change of velocity in mathematics and physics the term rate always means divided by time it's kind of like how fast something is changing so in this case it is the change of velocity over time the change of velocity here refers to the difference between the final and initial velocity that's why the formula for acceleration is final velocity minus initial velocity divided by time so the change of velocity is the final velocity minus initial velocity this can also be written using symbols of a = vus U / T where U is the initial velocity which means the starting velocity of the object V is a final velocity which is the ending velocity of that particular motion that we're observing and T is the time taken for this change in velocity that means the time taken for the object to change the velocity from U to become V the unit for acceleration is quite simply m/s squared some of you may be wondering why is it so unusual well it's because this is determined from the formula as you should know by now the unit for velocity is me/ second on the top part of the equation final velocity minus initial velocity both are me/ second the unit for time is second So based on the equation m/ second divided by second what you will end up getting is met per second squared that's why the unit for acceleration is me/ second squared now some of you might learn acceleration as the change in speed divided by time this is only true in certain syllabi for example if you are taking coordinated Sciences or combined Sciences however if you're taking SPM or igcs physics you'd have to learn it as a change in velocity over time please remember this as a change in velocity because acceleration is a vector that means it has magnitude and Direction and therefore to calculate the acceleration correctly you must use velocity which is also a vector now let's take a look at an example of how to apply this formula in this example this car starts from rest which means means the initial velocity of U is zero it increases its velocity and after 2 seconds it reaches the final velocity V of 10 m/s so to calculate the acceleration all you need to do is take these values and substitute them into the equation so we have a = 10 - 0 / 2 giving us acceleration of 5 m/s squared so because u and v are not the same they're changing right that means there is acceleration so here we can see that a positive acceleration means an increase in velocity the value for the acceleration we get is non zero because u and v are not equal so what if we get a situation where u and v are equal obviously that would be zero acceleration so this occurs when the object is moving with constant velocity where the final velocity and initial velocity are equal throughout the entire motion the object is moving with the same velocity that's why u and v are also equal so no matter what the value the time measured is you will get zero acceleration so keep in mind zero acceleration can mean two things one it can mean that the object is stationary so U is zero V is zero they're the same they're zero object is not moving so you get zero acceleration or as you can see from the explanation just now zero acceleration can also mean that the object is moving with constant velocity from start to end regardless of the time the object is moving with the same value of velocity bear in mind however that zero acceleration does not necessarily mean that the object is moving slowly this is a common mistake that a lot of students make an object can be moving at very high constant velocity at zero acceleration for example you can have a rocket moving at 2,500 m/ second that's incredibly High Velocity but it's moving at zero acceleration if the velocity is constant at 2,500 m/s from start to end of that particular motion so remember zero acceleration does not indicate the slow movement it just means the velocity is not changing now let's look at negative acceleration so first of all the concept of deceleration can be seen from this example say an object is moving with an initial velocity of 10 m/s and it slows down after 2 seconds it comes to a stop where final velocity V is zero so when you calculate the value of acceleration a you get 0 - 10 / 2 giving us -5 m per second squared because the velocity has decreased that's how we get a negative value of acceleration in this situation because the object is slowing down this is known as de acceleration however negative acceleration does not always necessary mean there is deceleration so in all the earlier examples we took the motion to the right as positive what if the object is moving to the left so if you remember what you've learned about vectors if it's moving in the opposite direction we would indicate that opposite direction with the symbol of negative so we can have a situation like this where an object is actually gaining speed but it's moving in the opposite Direction its initial speed is zero and its final speed is 10 but in this case because it's moving to the left which is the opposite direction the final velocity is actually -10 so when we calculate the acceleration we would get -10 - 0 / 2 giving us a value of -5 m/s squ the value here is identical to the value of the deceleration in the previous slide but the motion here is very different so in this case the car is actually not decelerating it's just that it's moving with negative acceleration in this case the negative acceleration here means an increase in speed but in the opposite direction so sometimes you can get two situations that are vastly different in terms of how we observe the actual motion but mathematically they appear to be identical so in case you're wondering oh my gosh how am I going to solve questions like this so when it comes to calculations don't worry just substitute the values in and that's the value you're going to be working with so mathematically the deceleration and negative acceleration could be the same it's just that an observation in real life they're different so for now if you're taking SPM and igcc physics don't worry so much about that all these complicated understanding of the mathematical numbers and actual motions will only take place at a higher level if you're going to pursue physics so for now just to complete this lesson when it comes to linear motion sometimes you could be asked to describe the motion so when describing motion typically you should have two different words one would indicate whether the value is changing or non-changing and also the type of motion the exception in this case is if the object is station because if it's stationary it's at rest it's not moving there is no need to describe the motion because it's not moving however if the motion involves speed velocity or acceleration ideally these types of motion should be accompanied by the descriptor of constant or uniform increasing or decreasing let's look at some examples so as you can see if the object is not moving you just need to mention that it's stationary next if the object's speed or velocity is not changing then you can say constant speed or constant velocity or you can also say zero acceleration by the way the terms constant and uniform mean the same thing so you can also write uniform speed or uniform velocity if the speed of velocity is increasing write that out increasing speed or increasing velocity if the velocity is changing at a constant rate that means it's moving with constant acceleration and that's another term you can also use if the speed of velocity is decreasing you can write decreasing speed or decreasing velocity if this decrease is at a constant rate then you can write constant deceleration and finally if the speed is increasing in the opposite direction you can write increasing speed in the opposite direction or constant negative acceleration so I hope you found this video educational and helpful please remember to click like and if you'd like to have access to more lessons Solutions and exam strategies do subscribe or check out my website physic rocks.com for the latest updates in the syllabus for SPM and igcc physics as well as access to latest video lessons happy studying