the first chapter in this first chapter will be talking about the motion in a straight line in order to understand the concept of motion we need to understand the basic fundamentals which are the distance and the displacement what's the differences between the distance and the displacement the the distance is the total length of the path travel as it says here the total length of the path travel the unit of the distance is the metre does the SI unit the distance is a scalar quantity that means it does not have any direction so it has only magnitude it does not have any direction and as the direction as as the distance does not have any direction it cannot be negative it's only positive so it can be either zero or it can be positive so that's about thee the distance now the displacement was the displacement it is a change in the position of the object if he travelled from one point to another point the Sothis distance between the two points the starting point and the end point the shortest distance gives you the the displacement or in other words the displacement is defined by this formula here this is the change in the position XF minus x0 X F is a final position an X 0 is the initial position and this is the Delta X this is called the Delta X which is the change the object the displacement is a vector quantity it has both magnitude and direction as this one has the direction it can be both positive it can be negative two so the difference between the distance and the displacement less here let's say you are moving in a circle all right and you started from point A so this is the starting point and then and this is the final point you started from point A and then you moved to the point B the path which and you moved along a circle that means you started moving this way all right and you moved from point A to point B in this case you have to calculate what is the distance and what is the the displacement okay so the distance the actual path you have traveled is all the way along this curved path along this semicircle here so this is the distance in other words the distance is in the actual path color and if I need to write it down the numbers the way you you have to write down is a 2 PI R divided by 2 the 2 pi R is the total circumference and the as we have more only the half of it it is divided by 2 so the 2 and 2 cancels out then you have pi times R the PI and the radius in this case is 5 meter so what is they say if we multiply them together what you get is fifteen point seven meter so this is the the distance now let's calculate the the displacement as I mentioned what is the displacement the displacement is the straight line connecting the starting point and the final point the starting point is this point a and the final point is this point B if I connect these two line this will be the the length of this line will be the displacement all right and this is the direction as well so what is the length of the line connecting initial point and the final point or what is the length of the line connecting the final point and the initial point so it is the length of a B which is equal to the diameter or twice up the radius the radius in this case is five meter so your total displacement is going to be ten meter so this is the one example all right so we have calculated distance and the displacement and look at the numbers the distance is fifteen point seven meter and the displacement is 10 meter so the distance in this case is greater than the displacement now let's take a look at the another example here now in this case the point the particle or an object is moving from point A to point B and then it is moving through the different paths here the path is shown this way so it starts moving this way and then moving this way all right now you have to calculate what is the total distance and what is the total displacement so that as by definition the distance is the total path cover so in this case the total path cover is this length Plus this length Plus this length this and this so if I need to add them together what I get is 2 meter plus 3 meter plus 2 meter plus 3 meter plus 2 meter okay if you add them together what's number I get get 5 5 10 to 2 meters so the total distance is 2l meter now let's calculate the displacement what is the what is displacement the displacement is again if we connect a line a straight line from point A to point B then this length this length yet which is shown by this arrow here gives you the total displacement so let's calculate the length here this length here what is this length here this length is 2 meter this is 3 meter and this is 2 meter so the total displacement is 2 plus 2 plus 2 this to the first 2 is this length the second 2 is this length here and that third one is this length so the total displacement is 6 meter this is the second example now let's move to another example here now in this case you start from point A and then you go to point B and the path it's on this way so you first travel from point A to this point and then from this point to the final point B and the various of routes are shown here now you have to what is the total distance and what is the total displacement the total distance is a three meter three meter plus two meter which is equal to so seven meter this is equal to seven meter and now the total displacement how do you define the total displacement the total displacement is defined as a straight line connecting the initial and the final point if I connect this point this length shown by the red color is the displacement so what is this value here if you look a triangle this is a right angle triangle so the total length would be 3 squared plus 4 squared which is 16 plus 9 so this will be 5 meter so in this case the displacement is 5 meter if we connect the initial point and the final point the length of the line connecting the initial point and the final point is the displacement now how do you find out the angle so the angle is defined as this angle now here let's call angle theta all right so the particle has moved or the object has moved from point A to point B in this direction or at an angle theta with respect to x-axis or with respect to the horizontal line so what is this angle here how do you find out the angle look at this triangle here but then the tangent of theta the tangent of theta is a rise over run 4/3 so the theta but with the tangent inverse 4/3 and if he's just solve it if you just solve it let me give you the number 4/3 shift tangent inverse you'll get 53 degree so this angle is fifty three point one three degree so what does this mean that means the particle moves from point A to point B at an angle of fifty three point two one three degree with respect to the horizontal line and it has moved five meter thus that's how you get from point A to point B all right now let me give you one more example the distance and the displacement the particle in this case has a started from this point a a and it has moved to the point B and the path is sewn here how do you calculate the distance so the distance is the total path cover this is 2 meter this is 1 meter and this is again and this is totally the 4 meter 2 meter 1 meter and the 4 meter 2 plus 1 plus 4 what you get is 7 meter dusty a distance now what is the displacement how do you define displacement the displacement is defined if you connect these two lines the length of this line gives you the magnitude of the displacement all right now we need to find out the length of of a B and then the angle and this will give you the angle okay so you see this is one meter this is one meter and as this is the total length so this will be the for two meter because from this point to this point is the four meter and from this point to this point is to 2 meter so this one will be 2 meter so the angle if you look at this triangle here let me erase this one let me find out the angle the angle now that is defined at the tangent of theta which is in this case P will be 2 meter divided by 1 meter then your angle theta would be equal to sixty three point one three we first calculate our D angle alright so in order to calculate so you just type to sift tangent inverse you'll get sixty three point four in fact for three degree and the displacement is a square root of 2 square plus 1 square and it will be a square root of 5 meter and the square root of 5 is 5 squared which with 2.2 tricks 6 2.2 4 meter it is this is the the displacement this is called the magnitude of the displacement and this is called the angle okay now the final example I'm going to give you a for the distance and displacement is let's say you're moving in a circle again and us started from point A all right and then and you started moving in a circle and then you again came to the same point or a starting point and the ending point is exactly the same and you're moving in a complete circle here move in a complete circle okay so what is the distance in this case the distance is a circumference the 2 pi R which is the length of a circle the 2 PI R so 2 pi and our radius is 10 meter if you solve this number if we multiply them together you'll get 20 times which is 62 point 8 meter 62.8 meter is the the distance and the displacement the displacement is if we connect the initial point and the final point in this case there is no length because the initial point and the final point is exactly the same so in this case the displacement is exactly 0 meter all right now let me give you one more example here let's say you have one particle you started there are two of two men both I started from the same point all right one point one object move this way that's a 5 meter and the another man moved this way exactly the same length 5 meter really the one person moved this way and this one okay let me change so this person moved this way and this person has moved this way so now what is the distance the distance for both the distance the actual path traveled by both men is exactly the same which is 5 meter and now the displacement let's call this is a let's call this an B so the for the displacement the displacement of a will be negative five meter and the displacement of be only positive five meter but the distance for both is exactly the same five meter and the reason is because we it is it does have the direction we can call this direction as a positive direction then we have to call the opposite direction as a negative reduction so as you see now the dis and the distance is always greater than or equal to the displacement a displacement can be positive it can be negative orchid it can be the zero all right it is a vector quantity displacement is a vector quantity while the distance I hope all the examples will help you to understand the difference between the distance and the displacement thank you so much