distance displacement speed and velocity in this special lecture you will learn something very awesome about different parameters of kinematics i will also teach you some unique concepts which 90 students are not understanding firstly let me teach you the basic concept of distance and displacement let's consider two houses these houses are connected by two different roads that this road is road number one and this road is road number two now one person uses this first road to go from this house to this house that he travels hundred meter while the second person used the second road to go from this house to this house let heat travel 70 meter now listen carefully we call road number one as distance so 100 meter is a distance between these two houses while we call road number two as displacement because it is shortest and directed path from one house to another so 70 meter is displacement according to these facts we define distance as the total path covered by a body in a given time is called distance let me repetite the total path covered by a body in a given time is called distance it is denoted by different letters like s x m etc its s a unit is meter while we define displacement as the shortest and directed path travelled by a body is called displacement let me repeat it the shortest and directed path travelled by a body is called displacement it is denoted by s arrow x arrow rm arrow its si unit is also meter in this lecture i will use s for distance and s arrow for displacement remember that distance is a scalar quantity and displacement is a vector quantity now here if i write s is equal to 100 meter our s error is equal to 70 meter can you differentiate between them well s is equal to 100 meter is a distance and s arrow is equal to 70 meter is a displacement here let me teach you one important question why distance is a scalar quantity and displacement is a vector quantity well consider the previous example we know that road 1 is a distance and row 2 is a displacement now listen carefully let two cars are moving between these two houses here at this point the direction of the car is like this at this point the direction of the car is like this and at this point the direction of the car is like this so we say that the direction of the car is constantly changing on road number one let me repeat it the direction of the car is constantly changing on road number one thus road number one has no proper direction it is a scalar quantity therefore we say that distance is a scalar quantity on the other hand at this point let the direction of the car is like this at this point the direction of the car is like this and at this point the direction of the car is also like this so we say that the direction of the car is not changing on road number two let me repeat it the direction of the car is not changing on road number two this road number 2 has one proper direction it is a vector quantity therefore we say that displacement is a vector quantity so noted down these important points let me teach you the basic concept of speed and velocity well it is super easy we define speed as the rate at which an object covers distance remember that in physics the word rate usually means divided by time so speed is equal to distance divided by time we denote speed by v so v is equal to s upon t the s a unit of speed is meter per second we have already learned that distance is a scalar quantity so speed is also a scalar quantity on the other hand we define velocity as the rate at which an object covers displacement we know that rate means divided by time so velocity is equal to displacement upon time we denote velocity by v arrow so v arrow is equal to s arrow upon time the s unit of velocity is also meter per second in a proper direction we have already learned that displacement is a vector quantity hence velocity is also a vector quantity just remember that speed is equal to distance upon time and velocity is equal to displacement upon time here let me teach you one important concept why we need to study speed and velocity well consider two cars that the speed of this car is 30 meter per second and the speed of this car is 40 meter per second notice speed that shows this car covers 30 meter distance in one second while this car covers 40 meter distance in one second here if i ask you 30 meter per second or 40 meter per second in which direction well speed cannot answer this question because speed is a scalar quantity it only shows how fast or slow an object is moving so here comes the part of velocity we can see that these both cars are moving towards right thus i say velocity of this car is v arrow 30 meter per second towards right and the velocity of this car v arrow is equal to 40 meter per second towards right therefore remember that speed only shows how fast or slow an object is moving it doesn't show the direction of motion like v is equal to 30 meter per second rv is equal to 40 meter per second while velocity show how fast or slow an object is moving plus it also shows the direction of motion like v is equal to 30 meter per second towards right and v is equal to 40 meter per second towards right now let me teach you different numerical problems of distance displacement speed and velocity to learn all these numerical problems you must understand the concept of parameter for example consider this circle now if i ask you to find its perimeter how can you calculate it well i take a rope and then i wrap it around this circle the total length of this group is equal to the perimeter of the circle let the length of this group is 1.3 meter so the perimeter of this circle is 1.3 meter just remember that perimeter is the length of a boundary of any shape let me repeat it perimeter is the length of a boundary of any shape now consider a circle let this man starts walking from point b move around the circle and come back to point b find its distance displacement speed and velocity well the person is working on the boundary or perimeter of a circle we know that the perimeter of a circle is 2 pi r thus the distance of the person s is equal to 2 pi r because he has walked on the boundary of a circle secondly remember this important point if initial and final position are the same displacement is zero because we say that body is not displaced at all here the initial and final position of the person is p so its displacement is zero thirdly speed is equal to distance divided by time here distance is 2 pi r i divide it by time so speed is equal to 2 pi r upon time fourthly velocity is equal to displacement upon time here displacement is zero so velocity is also zero but using this concept we can easily calculate distance displacement speed and velocity of any object in closed path like rectangle its perimeter is 2 into l plus b like circle its perimeter is 4 x like triangle its perimeter is a plus b plus c just noted down the perimeter of all these shapes now let me teach you exam questions consider that a car traveled from p to q in one minute calculate at speed and velocity well we know that the perimeter of a circle is 2 pi r here this is a semi-circle i divide the perimeter of a circle by 2. i get the perimeter of a circle is equal to pi r the car traveled from p to q along the perimeter of a semi-circle so the distance travelled by the car is equal to perimeter of the semi-circle which is pi r we know that the radius of the car is 100 meter and the value of pi is 3.142 after calculation i get s is equal to 314.2 meter so the distance travelled by the car is 314.2 meter we know that speed is equal to distance upon time here the distance is 314.2 meter and the time is one minute and one minute there are 60 seconds after calculation i get 5.23 meter per second so the speed of the car is 5.23 meter per second now what about displacement well the car is displaced from p to q in this direction so displacement of the car is equal to the diameter of the circle we know that diameter of the circle is 2r so displacement is equal to 2r here we are already given the value of r which is 100 meter i get displacement is equal to 200 meter thus the displacement of the car is 200 meter towards right or towards east we know that velocity is equal to s arrow upon time here the displacement is 200 meter and the time is given which is 1 minute or 60 second after calculation i get 3.33 meter per second towards east so by this way we can easily calculate distance displacement speed and velocity finally let me teach you one of my favorite questions a ball traveled 4 meter in eastern direction and 3 meter in northern direction in 2 second calculate its velocity well let me draw a freehand diagram we know that the ball traveled 4 meter in eastern direction and then 3 meter in northern direction we can see that this is the displacement of the ball now using pythagoras theorem we can calculate the displacement of the ball we know that pythagoras theorem is hypotenuse squared is equal to base squared plus perpendicular squared here displacement is hypotenuse the base is 4 meter and the perpendicular is 3 meter rs is equal to square root 4 squared plus 3 squared after calculation i get s is equal to positive negative 5 meter remember that displacement may be positive or negative but distance is always positive for example here in this direction displacement is positive 5 meter while in opposite direction displacement is negative 5 meter in this case i select this direction our displacement is equal to positive 5 meter we know that velocity is equal to displacement upon time our v is equal to 5 meter upon 2 second i get v is equal to 2.5 meter per second so the velocity of this ball is 2.5 meter per second therefore by this way we can easily calculate distance displacement speed and velocity