Motion in a straight line/Grade-11/Physics

Added: 2026-05-15

[00:01:23]Hello students.

[00:01:26]Welcome to the student in the brain.

[00:01:29]This is our sir.

[00:01:32]Today topic is motion in a straight line.

[00:01:36]Okay, let's discuss about it.

[00:01:42]Motion in a straight line.

[00:01:47]Hello students. Welcome to the student in the brain. This is our sir. Today topic is motion in a straight line. So, what is motion in a straight line?

[00:01:58]So, like normally, we know that light moves in a straight line path in a homogeneous medium.

[00:02:05]So, when you throw the object on the ground, so, it moves in a straight line path.

[00:02:12]Yes or no?

[00:02:13]So, in this topic, we'll completely discuss about velocity, acceleration, displacement.

[00:02:25]So, all those points we'll discuss in this motion in a straight line topic.

[00:02:34]Means, so, here, when you throw when you are throwing the object on the ground, if the object moves if the object moves on the ground, right? So, if you want to describe the position of the object, if you want to describe the position of an object, if it is required only one coordinate axis out of three coordinate, what are those?

[00:03:00]X axis, Y axis, and Z axis. Out of these three, if it is required only one coordinate to describe the position of an object, then we can say the body is moving in a straight line path.

[00:03:15]Right? Like in one dimension.

[00:03:19]Yes or no?

[00:03:21]Yes.

[00:03:22]Now, here, if the object is moving moving in a straight line, so, let's start motion in a straight line.

[00:03:34]Motion in a straight line.

[00:03:48]Okay. So, here, in this topic, we'll discuss about distance distance second one displacement displacement and third one is speed fourth one is velocity and then coming to fifth one is acceleration So after that equation of motions we'll discuss equations of motion. First of all, what is a distance?

[00:04:28]Okay, so I want to move from point A to point B.

[00:04:33]This is the point A and point B.

[00:04:36]Like initial position, final position also we can say.

[00:04:40]Initial position and final position point A, point B.

[00:04:46]Okay, starting point, ending point.

[00:04:49]Like that we can discuss.

[00:04:51]Like that we can take.

[00:04:53]Right? So I want to move from point A to point B.

[00:04:59]So how many ways I can go from point A to point B? So I can go I can travel in this path.

[00:05:07]I can travel in this path. I can travel in this path. Like that many ways.

[00:05:14]Many ways I can go, right? So I can go like this, like this, like this.

[00:05:20]So generally there is one uh uh like a point general here this is the home and this one is the college.

[00:05:39]Okay, normally if it is a walkable distance if it is walkable distance from home to college directly will go.

[00:05:50]While coming to college to home, so we'll go like this, like this, like this, like this, like this, like this, like this. Or sometimes like this, like this, like this, like this.

[00:06:01]Okay?

[00:06:03]So, we'll identify number of paths.

[00:06:07]Yes or no? From reaching college to home.

[00:06:12]But home to go home to college direct path.

[00:06:15]Going right? So, time is not there that time. So, we have to go uh directly from home to college. But whereas college to home, so after completion of college, we'll take long path to reach the home.

[00:06:32]Yes or no?

[00:06:33]Okay? So, it take too much time to also.

[00:06:36]Okay, then. Apart it, come to the point.

[00:06:39]Um What are the path the object is taking to move from initial point to final point or or uh like a starting point to ending point, what are the path the object is traveled? Okay? So, the total length of the path covered by an object is called distance.

[00:07:04]So, either in this path or this one, we'll give numbering. Either 1 2 3 4 5 6 7. Out of seven paths, if any path object is followed, okay? The total length of the particular path followed by an object to reach from initial point to final point, initial point to final point, starting point to ending point.

[00:07:35]Okay? So, that distance that length of the path is called distance. And here, it has only magnitude.

[00:07:44]So, in the previous ex- uh like in previous topic like vectors and scalars in my vectors and scalars topic. Uh so, I given brief note about a mass scalars and vectors.

[00:08:00]Like a scalar has magnitude.

[00:08:03]Okay, it has only magnitude.

[00:08:05]And coming to the vector, it has both magnitude and direction.

[00:08:09]So, here you can observe it has only magnitude from point A to point B.

[00:08:15]From point A to point B, it has only magnitude.

[00:08:19]It doesn't have any direction. So, if it is goes in a straight path from point A to point B, then we can follow. But, what are the path followed by an object is called distance, and then the total length.

[00:08:31]The total length of the path covered by an object, that is called distance.

[00:08:37]Okay, it has only magnitude.

[00:08:39]And whereas, velocity velocity, if you see, the shortest path from initial point to final point.

[00:08:50]Okay, so straight path.

[00:08:53]Straight path from point A to point B.

[00:08:57]The shortest distance from initial point to final point is called displacement.

[00:09:03]Displacement is a vector quantity. So, why displacement has why we are calling displacement as a vector quantity? Because it has both magnitude and direction.

[00:09:16]It has both magnitude and direction.

[00:09:20]So, magnitude is there as well as particular direction.

[00:09:24]Okay, so in particular direction, the object is moving. That's why displacement is a vector quantity.

[00:09:31]Whereas, speed is a scalar quantity.

[00:09:35]Uh so, still we have to talk about speed.

[00:09:38]First, we will discuss about distance and displacement. And we will do one problem.

[00:09:45]Like one example problem we'll do it.

[00:09:48]Okay?

[00:09:50]So, during a round trip during a round trip, so here you can see the object is started from point A and reached it to point B.

[00:10:06]So, object is started from point A to point A and reached to point B. So, in this case what is the distance? Point number one.

[00:10:19]So, second one is what is the displacement?

[00:10:25]If it is half circle here you can see from point A to point B, you can observe this one.

[00:10:34]This one is the shortest distance shortest distance.

[00:10:38]So, here we can say displacement from point A to point B and this one is the distance.

[00:10:49]Understood?

[00:10:51]So, from point A to point B is called displacement because the shortest path from initial point to final point.

[00:10:59]And so, the body is traveled from point A to point B, right? That is the distance.

[00:11:05]That is the distance.

[00:11:07]So, now you say so, total is 2πr.

[00:11:11]Perimeter of the circle is 2πr. Half of the circle is πr.

[00:11:17]So, if it is uh radius, we can say this is a diameter r r.

[00:11:27]Okay, from point A to point B.

[00:11:30]So, distance is πr.

[00:11:33]Displacement is r + r.

[00:11:38]So, r is radius. This one also radius.

[00:11:42]So, displacement is 2r.

[00:11:46]Distance is πr.

[00:11:49]So, I hope it is very clear.

[00:11:52]So, if it is complete circle So, the body is started from point B point A and reach it to point A same.

[00:12:00]So, it started from point A and reach it to point A only.

[00:12:05]So, in this case, what is distance? And what is displacement?

[00:12:10]Distance is 2πr.

[00:12:13]Displacement is zero.

[00:12:17]Why?

[00:12:18]Displacement is nothing but as I mentioned the shortest path from initial point to final point.

[00:12:25]So, the body is started from point A and reach it to point A.

[00:12:30]Then then displacement is zero and distance is 2πr perimeter of the circle.

[00:12:39]Understood or not?

[00:12:41]So, I hope it is very clear.

[00:12:43]And one more point we'll discuss.

[00:12:49]One more point.

[00:12:59]So the body is started and moved So, here north, south, east, west.

[00:13:10]So, 5 m towards east.

[00:13:14]After that 5 m towards north.

[00:13:20]Okay, so body is traveled 5 m towards east.

[00:13:25]After 5 minutes, again it traveled towards north.

[00:13:35]Okay?

[00:13:36]So, here you can see like this.

[00:13:42]Understood or not?

[00:13:49]So, I hope it is very clear.

[00:13:51]North, south, east, west.

[00:13:55]So, here you can observe So, 5 m towards east, 5 m towards north.

[00:14:09]Now, we have to find out First one is First one is distance.

[00:14:21]Second one is displacement.

[00:14:29]Can you identify what is a distance and what is a displacement?

[00:14:35]So, distance is Okay, so distance and displacement.

[00:14:52]Distance is 5 + 5.

[00:14:55]10 m.

[00:14:57]Whereas displacement, so if you are taking X, according to Pythagoras theorem, X ^ 2 = 5 ^ 2 + 5 ^ 2.

[00:15:09]Then X ^ 2 = 25 + 25.

[00:15:13]So, X ^ 2 = 25 * 2.

[00:15:18]So, X ^ 2 = 5 root 2.

[00:15:21]Sorry, X equal to 5 root 2.

[00:15:24]Is it clear?

[00:15:26]Root 25 5, so anyway root 2 will get.

[00:15:31]Understood or not? So, like this we have to do it.

[00:15:35]Like this we can do it.

[00:15:39]Understood or not? So, this is about distance and displacement.

[00:15:44]Distance and displacement.

[00:15:47]Okay?

[00:15:49]Next.

[00:16:08]So, next one we'll discuss about uh speed. Yeah.

[00:16:17]Speed.

[00:16:22]Speedy nothing but distance by time taken.

[00:16:28]First one is distance by time taken is called speed.

[00:16:35]Distance by time taken is called speed.

[00:16:38]SI unit of speed is meter per second.

[00:16:42]And units are m ^ 0 l ^ 1 t ^ -1.

[00:16:50]And coming to the fourth one, so speed is a scalar quantity.

[00:16:57]What is that? Speed is a scalar quantity.

[00:17:03]So, understood or not?

[00:17:04]Speed equal to distance by time taken.

[00:17:08]SI unit of speed is meter per second.

[00:17:12]And we can observe dimensional formula.

[00:17:20]Here m power zero, m power zero, l power one because distance is there.

[00:17:25]Here we can write l by t.

[00:17:29]l by t we can write.

[00:17:32]Like this.

[00:17:34]l by t.

[00:17:35]m power zero. So anything we can take m power zero, l power zero, t power zero, k power zero equal to one.

[00:17:46]Understood or not? So because there is no mass.

[00:17:51]Mass is not there. Only length and time.

[00:17:53]So that's why m power zero, l power one, t power minus one.

[00:17:58]And coming to this one.

[00:18:01]So speed is a scalar quantity.

[00:18:04]Why speed is a scalar quantity?

[00:18:07]It has only magnitude. It doesn't have any direction.

[00:18:11]So because distance by time taken.

[00:18:14]Understood or not? So I hope it is very clear. What are the points we discussed?

[00:18:19]Distance, displacement, speed.

[00:18:22]Okay, coming to the velocity.

[00:18:24]So here we have to discuss about few more points.

[00:18:29]Those are One is the average speed.

[00:18:49]Second one is instantaneous speed.

[00:18:56]And third one is uniform speed.

[00:19:00]Uniform speed.

[00:19:03]And the fourth one is non-uniform speed.

[00:19:10]Non-uniform Okay, so these are the points we have to discuss.

[00:19:19]So, the average speed total distance by total time taken.

[00:19:24]Average speed is nothing but total distance by total time taken.

[00:19:30]And instantaneous speed So, generally instantaneous speed means speed at particular instant.

[00:19:37]So, normally like a flash, you know, right? Flash. So, suddenly at the particular point, what is speed of the speed of an object is called instantaneous speed.

[00:19:50]And you can observe So, you are standing in the railway track, so railway platform.

[00:19:57]So, you are standing in the railway platform.

[00:20:00]Okay, so the train is moving on the railway track.

[00:20:03]Okay, so at the particular instant, suddenly like this.

[00:20:09]Okay, suddenly it moves very fast.

[00:20:12]At particular instant, if you observe at particular instant, what is speed of an object? Speed of the train is called instantaneous speed.

[00:20:22]Okay?

[00:20:23]So, among us uh super super super people will be there. So, they like to uh move very fast.

[00:20:35]Yes or no?

[00:20:36]Like So, they develop that habit.

[00:20:41]Okay? So, doing little more fast than usual.

[00:20:49]Understood or not? Okay, so come to here. That is instantaneous speed.

[00:20:53]Coming to uniform speed.

[00:20:55]So, body covers equal distance in equal interval of time.

[00:21:00]Body covers equal distance in equal interval of time.

[00:21:08]Body covers equal distance in equal interval of time, that is called uniform speed.

[00:21:14]Coming to non-uniform speed, body covers unequal distance in equal interval of time or equal distance in unequal interval of time. One must be unequal.

[00:21:26]So, if speed is equal, time must be unequal.

[00:21:30]If speed is unequal, time must be equal.

[00:21:36]Either if you take any one unequal, then that is non-uniform speed.

[00:21:42]Uniform motion, non-uniform motion, like that also we can discuss.

[00:21:46]Okay? So, the these points will be discussed for velocity and acceleration, too.

[00:21:54]So, velocity we'll discuss now.

[00:21:57]Later, we'll go to the acceleration.

[00:22:00]Okay? So, let's start.

[00:22:13]Velocity.

[00:22:21]Velocity is nothing but a average velocity, instantaneous velocity, uniform velocity, and a non-uniform velocity.

[00:22:40]So, velocity is nothing but displacement by time taken.

[00:22:46]Velocity is nothing but displacement by time taken. SI unit of velocity is meter per second.

[00:22:53]So, yeah, SI displacement by time taken, yeah, meter per second, and damage formula is M power zero, L power one, T power minus one.

[00:23:06]And velocity is a vector quantity.

[00:23:09]Sir, why velocity is a vector quantity?

[00:23:12]Because it has both magnitude and direction.

[00:23:16]So, velocity has both magnitude and direction. That's why it is a vector quantity.

[00:23:24]Understood or not? So, I hope it is very clear now.

[00:23:27]The average velocity.

[00:23:30]So, total displacement by total time taken, or net displacement by total time taken is called average velocity.

[00:23:39]The average velocity. Coming to instantaneous velocity.

[00:23:44]So, velocity at that particular instant.

[00:23:48]Okay, so you can observe you're hitting the ball. Okay, so uh when the bat is moving like this, the ball is coming like that. So, at that particular instant at that particular instant, what is the velocity of the bat, uh velocity of the ball, we can say instantaneous velocity.

[00:24:10]And coming to the uniform velocity. And here one thing you need to observe, so as I mentioned, so both must be equal.

[00:24:19]Body covers equal displacement in equal interval of time.

[00:24:24]So, there in the speed I mentioned equal distance.

[00:24:28]In velocity I'm mentioning equal displacement.

[00:24:32]Okay? So, in uniform, both must be equal. Equal displacement in equal interval of time.

[00:24:39]And coming to the non-uniform velocity.

[00:24:43]Non-uniform velocity means body covers equal displacement in unequal interval of time, or unequal displacement in equal interval of time.

[00:24:55]That is called non-uniform velocity.

[00:24:59]Okay, one must be non- One must be not equal.

[00:25:04]Okay, so it must be unequal. So, suppose you are taking velocity. Okay, so equal displacement in unequal interval of time uh equal time unequal displacement Anyone must be unequal.

[00:25:25]Then remaining thing will be same.

[00:25:28]Okay, so I hope it is very clear.

[00:25:30]Understood or not? Velocity, average velocity, instantaneous velocity, uniform velocity, non-uniform velocity.

[00:25:36]And coming to acceleration So, we'll discuss about acceleration.

[00:25:41]Let's start.

[00:25:43]Acceleration is nothing but change in velocity by time taken.

[00:25:48]Acceleration equal to change in velocity by time taken.

[00:25:59]So, point number one change in velocity by time taken.

[00:26:11]And coming to the second one Here we can write a equal to v minus u by t.

[00:26:18]In the vector form v bar So, a bar equal to v bar minus u bar.

[00:26:25]So, it is in the form of It is in the form of vector notation.

[00:26:35]And coming to the third one So, meter per second squared.

[00:26:41]And coming to the fourth one So, dimension formula m power zero l power one t power minus two.

[00:26:51]Because length is l, time t squared, so m power zero so M power 0 L power 1 T power minus 2.

[00:26:59]And then coming to the fifth one, so acceleration is a vector quantity.

[00:27:07]Acceleration is a vector quantity. I hope it is very clear.

[00:27:12]Sure?

[00:27:13]Just check once.

[00:27:15]Acceleration is nothing but change in velocity by time taken, so vector notation. Acceleration is meter per second squared.

[00:27:23]And coming to the dimensional formula, M power 0 L power 1 T power minus 2.

[00:27:27]Acceleration is a vector quantity.

[00:27:31]And coming to the four points again here, again four we have to discuss. What are those?

[00:27:46]Point number one, point number one, the average, point number two, instantaneous, point number three, uniform, point number four, non-uniform.

[00:28:08]Non-uniform.

[00:28:11]So, the average nothing but So, the total change in velocity by total time taken.

[00:28:19]So, the average nothing but total change in velocity by total time taken.

[00:28:23]Coming to instantaneous, instantaneous acceleration means acceleration at that particular instant.

[00:28:31]Acceleration at that particular instant.

[00:28:34]And coming to uniform acceleration, body covers equal change in velocity in equal Body covers equal change in velocity in equal interval of acceleration.

[00:28:50]Coming to non-uniform acceleration, body covers equal change in velocity in unequal interval of time or unequal change in velocity by equal interval of time. As I mentioned, any one must be unequal.

[00:29:12]Okay.

[00:29:13]So, in uniform, both must be equal.

[00:29:17]And instantaneous instantaneous speed, instantaneous velocity, instantaneous acceleration.

[00:29:24]And coming to the average speed, average velocity, average acceleration.

[00:29:30]Okay. So, right from starting, distance.

[00:29:34]So, the total length of the path covered by an object is called distance.

[00:29:39]So, distance is a scalar quantity.

[00:29:42]And SI unit is meter.

[00:29:45]Dynamic formula is capital L.

[00:29:48]Okay.

[00:29:50]And coming to displacement, displacement is the shortest path from initial point to final point is called displacement.

[00:29:58]Displacement is a vector quantity.

[00:30:01]Dynamic formula is capital L.

[00:30:04]And Okay. So, coming to the next one, speed, distance by time taken, velocity, displacement by time taken, acceleration is change in velocity by time taken.

[00:30:15]So, these are all points related to distance, displacement, speed, velocity, and acceleration.

[00:30:25]Now, Now, equations of motion.

[00:30:39]Equations of motion by calculus method uh uh graphical method calculus method or graphical method Both I'll discuss.

[00:30:59]Okay?

[00:31:00]So, both I'll discuss. Let's see here.

[00:31:04]Here I can say a equal to dv by dt Then, uh So, dv equal to a into dt integral So, body starting from initial velocity reaching final velocity acceleration a time t Understood or not?

[00:31:27]So, then integral you have to take initial to final limits.

[00:31:33]Initial velocity, final velocity final velocity So, a integral 0 to t dt starting So, 0 time Uh next one uh final velocity t Now, you can take So, you can take t0 and t1.

[00:31:52]Uh 0 to t That's your choice.

[00:31:55]Now, we are taking uv a into t So, 0 to t 0 to t Then, you'll get v minus u equal to v minus u equal to v minus u equal to a into t equation one Then, we can also write uh u plus at.

[00:32:28]So, make it this one as equation one.

[00:32:32]Okay?

[00:32:33]So, now you can see uh So, this can be written dx by dt equal to u plus at.

[00:32:44]dx equal to u plus at into dt.

[00:32:50]So, integral 0 to x dx integral 0 to t u plus at.

[00:32:57]Then x equal to ut plus half at squared equation two.

[00:33:05]Then you can take this equation square on both sides.

[00:33:11]Okay, so here you can observe.

[00:33:13]So, v equal to u plus at, v equal to u plus at.

[00:33:18]That I'm taking dx by dt equal to u plus at.

[00:33:22]So, dx equal to we are taking cross multiplication u plus at into dt integral 0 to x.

[00:33:30]Then you'll get x equal to ut plus half at squared equation two.

[00:33:35]Okay.

[00:33:40]So, I hope it is very clear. Understood or not?

[00:33:42]So, a equal to dv by dt, dv equal to a into dt integral u to v. So, then we'll get equation of motion, first equation of motion. v equal to u plus at, x equal to ut plus half at squared.

[00:33:56]Now, you can take square on both side.

[00:34:00]If you are doing square on both side, v squared equal to u plus at whole squared.

[00:34:08]v squared equal to u plus at whole squared.

[00:34:12]Understood or not?

[00:34:13]So, then v squared equal to u squared plus a squared t squared plus 2 u a into t.

[00:34:22]Then v squared equal to u squared plus 2 a common.

[00:34:27]Then you'll get ut plus half at squared.

[00:34:32]ut plus half at squared.

[00:34:35]What do UT plus half 80 square? So, we got it X.

[00:34:40]Yes or no?

[00:34:42]So, then we'll get uh V squared equal to U squared plus 2ax.

[00:34:51]That's the equation of motion.

[00:34:53]Third equation of motion.

[00:34:56]Understood or not? So, just check once.

[00:34:59]Just check once.

[00:35:02]Is it clear or not?

[00:35:07]Is it clear or not? Just check once.

[00:35:17]So, next one same equation of motion by graphical method.

[00:35:24]Equation of motion by graphical method we'll discuss.

[00:35:28]Okay, let's start.

[00:35:31]Equation of motion by graphical method.

[00:36:02]So, velocity on Y axis, time on X axis.

[00:36:07]Velocity on Y axis, time on X axis.

[00:36:11]Okay?

[00:36:12]So, same the body starting with initial velocity U reach it to final position.

[00:36:17]So, I'm taking this as position A, position B, final velocity with respect to time acceleration A.

[00:36:25]Okay?

[00:36:26]So, it in with certain distance. Yes.

[00:36:30]So, change in velocity is there acceleration.

[00:36:33]Acceleration is there. So, it travel certain distance automatically with respect to time only.

[00:36:39]Okay. So, this is the point A.

[00:36:41]I'm taking point A and here is point B.

[00:36:46]Understood or not? Here I can take C D zero.

[00:36:52]So, this component is time T T. So, initial velocity is U.

[00:37:00]And final velocity is V.

[00:37:04]And coming to the change in velocity, what is change in velocity? V minus U.

[00:37:11]Okay.

[00:37:15]So, I hope it is very clear. Understood or not?

[00:37:18]Yes. Now, we can take from velocity time graph.

[00:37:25]From velocity time graph, okay. So, distance and uh time velocity time also we can take here.

[00:37:36]We can consider slope of the graph.

[00:37:41]Slope equal to So, here we are taking slope.

[00:37:48]What is that one?

[00:37:51]This one we have to take.

[00:37:53]That is BC by AC.

[00:37:57]BC by AC. BC is nothing but final velocity minus initial velocity.

[00:38:03]So, uh your slope is acceleration V minus U by T.

[00:38:07]Then you'll get V equal to U plus AT, equation one.

[00:38:16]And the next one, so we have to take distance and time graph, distance and time relation from velocity time graph only distance and time relation.

[00:38:29]Then we can take area of rectangle.

[00:38:33]Area of rectangle OACD.

[00:38:38]Area of rectangle Area of rectangle OAE CD plus area of triangle Area of triangle triangle A BC Okay, so now we can take S equal to U into T plus half into T into so V minus U is A into T.

[00:39:30]S equal to UT plus half AT squared.

[00:39:34]So this is equation of motion two.

[00:39:39]Okay, so this is second equation of motion.

[00:39:44]This is the first one and coming to the second one.

[00:39:48]So next third one is So area of the trapezium parallel sides OA U Okay.

[00:40:04]minus V So plus V by So base is OD that is nothing but time T.

[00:40:15]Time T by two So, s equal to u plus v.

[00:40:21]So, from this equation, what is the time?

[00:40:24]T, okay. So, from here directly we can write t equal to v minus u by a.

[00:40:31]T equal to v minus u by a. So, we can substitute here v minus u by a.

[00:40:40]Then you'll get s equal to v squared minus u squared by 2a.

[00:40:45]Then v squared minus u squared equal to 2as.

[00:40:49]So, that is the third equation of motion.

[00:40:54]Understood or not?

[00:40:56]So, third equation of motion.

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[00:41:07]So, I hope it is very clear.

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[00:41:25]Thank you.