This video explain the difference between distance and displacement in an outstanding way. Provides many examples which makes the concept very clear to the students.
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00:00Today, I am going to teach you the topic distance and displacement.
00:08This video is by RBA Educational Academy.
00:12Please viewers, I request you to watch the video from the beginning till end.
00:22Now I will define distance.
00:25How we can define distance?
00:29Distance is the path covered by the object in motion irrespective of the direction of
00:38path.
00:39Here the most important thing, what is that?
00:43Distance is the total path covered by the object in motion irrespective of direction.
00:52Now suppose if we start from the point A, if a body start from the point A and this
01:03body has to reach point B, it can travel in straight direction.
01:13It can travel from point A to B in straight direction.
01:18So suppose a person is travelling from point A, it want to reach point B in straight direction.
01:31Now this body can reach in zigzag way also, zigzag manner also, like this also in many
01:39ways.
01:40Now distance is the total path covered by object in motion irrespective of direction.
01:47If we see in case 1, here the direction is not in a particular, body is not moving in
01:58a particular direction.
01:59Here the direction of the body is different and it goes down, the direction changes, again
02:07the person moves up.
02:09So there is continuous change in direction.
02:13So here we do not consider, when we talk about distance, we do not consider direction.
02:18Therefore we can say that it is a scalar quantity.
02:26It has only magnitude without any direction, the total path covered by the body.
02:31Suppose this path covered, suppose the path covered is equal to 20 meters.
02:39So we can write S is equal to 20 meters, here we are taking the unit as meter, 20 meters.
02:48Now here we do not consider the direction but when we take the second case, this was
03:03about the distance.
03:12Now but if we consider these two points A and B and if the body moves in straight direction,
03:29if it travels in a straight direction from one point to another point.
03:38So here we have both magnitudes, suppose the distance S is equal to 10 meters, previously
03:48while explaining distance I told 20 meters.
03:51Here I will put one arrow also, this arrow tells us that it is a particular direction.
03:58So it has both magnitude and direction, therefore displacement we call it as a scalar quantity.
04:10Displacement is defined as the total change in object position along with the direction.
04:16So here the total path change in object position along with the direction.
04:34So when you move from one place to another place, everything changes.
04:40Suppose point A is in your home and point B is the crown present outside your home.
05:01So when you move from one place to another place, the complete surrounding changes.
05:08So change in position means the surrounding also changes.
05:11But it has a particular direction, we are moving in a particular direction.
05:14So displacement is defined as a change in the object position along with direction of
05:20motion.
05:21Or you can say the shortest path travelled by the body, the shortest path travelled by
05:26the body that is known as what we call as displacement.
05:34It is a vector quantity.
05:36Now distance, it can be positive, it can never be zero or negative.
05:57What we are saying here is be careful what I am speaking, you should listen very carefully.
06:04It can only be positive, yes.
06:08When you move from one point, any one point to any other point, suppose from P, I take
06:19a point P, I take a point Q and I am moving like this, like this, like this, like this,
06:25like this and reaching point Q.
06:28I am moving, I am travelling along this path.
06:34So I am moving distance, it has magnitude.
06:43So we can say the value is positive but it cannot be, it never be, it cannot be zero
06:56or negative.
06:57It is not, we cannot say, it cannot become zero, you move some distance from here to
07:04here, you travel, you walk some distance or you move by car, you are travelling some distance
07:09so it is always positive.
07:13It cannot be zero or it cannot be below zero.
07:17So keep this in mind.
07:19So distance is a scalar quantity, it can only be positive, it can never be negative or zero.
07:31But when we talk about displacement, here the scene is little bit different.
07:37I will tell you how, how can the displacement become zero.
07:43Suppose, what I should say, suppose if I take a number line and suppose this is the
07:52beginning that is zero, if I take 1, 2, 3 and 4.
08:03Now I start from this point, I travel from here like this, like this and I reach till
08:144.
08:15So the distance covered, I covered here 4 units, S is equal to 4, the distance is 4.
08:26But now I will explain you displacement, okay.
08:36If the person returns, if the person goes in this direction, 0 to 4 and the person comes
08:43back again from 4 to 0, then the distance will be 4 plus 4, distance covered is 8.
08:54But when we talk about the displacement, when we go from 0 to 4, we take plus 4 and
09:03when he moves in opposite direction from 4 to 0, we take minus 4, we consider the direction
09:11here.
09:12So here 4 plus time minus plus when you multiply with minus is minus 4, minus 4 is equal to
09:210.
09:24If I move further like minus 1 and minus 2 suppose, so I am erasing this distance, now
09:34I am explaining to you only the displacement here minus 1, here minus 2.
09:42So this person started from 0, it moves to 4, I have taken 4, okay.
09:47But suppose this person returns, okay, it turn backs again from 4, okay, it moves back
09:55to 0, then again it continues the journey and it reach minus 2, this point.
10:04So how many steps it moves?
10:061, 2, 3, 4, 5, 6.
10:11It moves 6 steps in opposite direction.
10:14So 4 plus minus 6, that is 4 plus time minus is minus 4 minus 6, when we subtract, okay,
10:29we see the bigger number minus smaller number 6 minus 4 is 2, sign of bigger number here
10:35is minus, so minus 2.
10:39So displacement we say minus 2.
10:42So displacement can be negative, displacement can be 0, displacement can be positive.
10:55If we consider that the this person move and stop at 4, displacement is 4, distance is
11:03also 4, but when it moves back again reach the same point in the straight direction,
11:11the sign become opposite, plus 4 it become minus 4, 4 minus 4 is 0, that means you can
11:17say when a body start from a point and come backs to the same point, okay, then the displacement
11:24will be 0.
11:27Now I am going to show you the, explain you the concept of distance and displacement by
11:36taking the right angle triangle.
11:38So here I have taken right angle triangle, the, this box, small square here, this indicates
11:46how many degrees boys, it indicates 90 degrees, you know, and in right angle triangle this
11:52will always be opposite to the longest side, which is not happening.
11:58Suppose I take this point as A, this point as B, and this point as C. Suppose we are
12:05traveling in a car and we have to reach point C. So if you want to find out how you can
12:12travel in a car from point A to point C, this is the shortest path travelled by the body.
12:21This will give you AC, means displacement, AC, AC is what, AC gives you displacement,
12:30I can say S, above I will put arrow, that is shortest path travelled by a body.
12:39But if I want to calculate the distance, I have to find out the, we are moving car from
12:44A to B, suppose it is 3 kilometer, then from B again we will move to point C, suppose this
12:52is 4 kilometer, so the distance covered by the body is AB, that is 3 kilometer plus BC,
13:03that is 4 kilometer, 3 plus 4, that is nothing but 7 kilometer, the distance is 7 kilometer.
13:14This is denoted by S, that is distance, we say distance is 7 kilometer. But what about
13:23the displacement? Distance is equal to 7 kilometer, okay. So the total path covered by a body,
13:32here the direction, we change the direction, okay, we move in this direction, then again
13:37we change the direction, okay. So this is a scalar quantity, distance is a scalar quantity
13:42and what is the total distance covered? Total path covered 3 kilometer plus 4 kilometer,
13:47it is equal to 7 kilometer. But this is not the case of displacement. Displacement means
13:53the shortest path covered by the body. So we move from point A to C, directly, we do
14:03not take this path A to B, that is 3 kilometer and B to C 4 kilometer, not like this, we
14:09will move directly from A to C. So we can find this value AC, this AC how we can find?
14:18By using the Pythagoras theorem. The Pythagoras theorem says that the square on hypotenuse,
14:25the square on the longest path AC is equal to the sum, sum means we will add, what we
14:31will add? The square of other two sides, that means we will add square of AB plus
14:42square of BC. Now boys, see, what is AB? What is the value of AB? 3 kilometers, okay, 3
14:52square plus, what is BC? 4, 4 square, 3 square means we multiply 3 two times, when we see
15:02the power 2, that means the base is multiplied two times, 3 multiplied with 3 is 9, of course,
15:10like that 4 multiplied with 4 is 16, when you add 9 and 16 is 35, this is AC square
15:20my boys, remember this is not our answer, our answer will be AC. So when we remove square
15:28from AC, from left hand side, we get square root on right hand side, that is square root
15:35of 25, the calculator will give you the answer, it is 5, but how we get that? We get 25 can
15:44written as 5 times 5, 5 multiplied with 5, the square root will be 5, 5 kilometer. So
15:55distance is 3 plus 4, 7 kilometer, it is a long, long path and the shortest path, what we get?
16:03We get shortest path as 5 kilometer. Still some boys, they will get confused, how you get out of
16:132 tau 5, so why you have taken 1 5 out of the root? They will get confusion in this part,
16:22because they don't, they lack the basic information. 5 multiplied with 5, we can write as 5 square,
16:29this radical sign root, means the value of this square root is, in the power, it is equal to
16:42half, that means 5 power of 2, we multiply this power 2 times 1 over 2, this 2 and 2 get cancelled,
16:565 to the power of 1, that is nothing but 5, that is 5 kilometer, displacement is the shortest path
17:06and it has a particular direction, so therefore it is a vector quantity. Now suppose I start from
17:13this point, so I want to complete a circle, suppose I complete a circle, now I am moving
17:21in this direction boys, I started from this point, now I covered the whole circle, I move along,
17:34this path and reach again to the same point. Now I will ask you what is the distance and what is
17:51the displacement, so think for a minute till I write here, what is the distance and what is
18:04the displacement, do you have any idea, I just explain you, displacement, now remember the
18:17definition of distance, what is the distance and what I told you about the distance, distance can
18:22be positive, it cannot be zero or it cannot be negative, so we are traveling here in the form
18:30of circle, we are covering a circle, so what is the circumference of circle, circumference of
18:35circle is 2 pi r, the total distance traveled by the person is circle, so when we move along the
18:45circle, the perimeter or the circumference is 2 pi r, so distance traveled is 2 pi r and we start
18:51from this point and we reach the same point, therefore we can say the displacement is zero,
18:58what is the displacement, zero, when a body start from a point, travel and reach the same point
19:10again, then the displacement will be zero, okay, suppose I start from a point and I complete a
19:21semicircle, now suppose I start from a point and move along this direction, I am moving along this
19:34direction, so a person start from this point and he moves along this direction and he reach this
19:43point, okay, you start from A and you reach point B, what is the distance, distance is, what is the
20:02distance boys, till the time I write, just tell me what is the distance and what is the displacement,
20:13I want to know from you what is the distance and what is the displacement, so boys, distance,
20:30when we talk about distance, distance is we cover from, we move from this point in the curve path
20:37from point A to B, that is semicircle, we are taking semicircle, we are talking about semicircle,
20:44when we cover a circle, the total distance is circumference 2 pi r, when we say semi,
20:51we divide by 2, 2 pi r divided by 2 that is nothing but distance is pi r, but when we talk
21:02about the displacement, the shortest path, see we start from here, from here this point A and we
21:10reach point B, okay, so this is the diameter, okay, what is the diameter from here to here,
21:18radius is r, here to here, center to this point, radius is r, so diameter is nothing but twice of
21:25radius, so displacement is diameter that is nothing but r plus r, so the displacement of
21:35the body is 2r, the shortest path in a particular direction, a vector, displacement is a vector
21:42quantity, it has both magnitude and direction, distance does not have the direction, it has only
21:51magnitude, so distance of semicircle, in case of semicircle, semicircle, the distance is pi r and
22:02the displacement is 2r, and in case of circle, the distance is 2 pi r and displacement is 0,
22:11so remember now, these are the differences of distance and displacement, so thanks for
22:20watching the video by RBA educational academy, I request you to please like, share and subscribe.