Uniform vs Non uniform

Uniform vs Non uniform


You must have seen this before. This is the speedometer of a car. It tells us the speed of the car while the car is moving. It shows that the speed of the car is not constant but it keeps on changing. Well this is the case with most of the objects in real life. The speed is not constant it keeps on changing. Now observe the motion of this boy. He moves from zero meters to ten meters in one second. From ten meters to twenty meters in the second second. In the third second, he covers another ten meters. Whereas in the fourth second he covers another ten meters. So this table represents the movement of the boy. It shows that in the time interval zero to one seconds that is time taken is one second. The distance travelled was ten meters. In the time interval one to two seconds when the time taken was one second the distance travelled was ten meters and so on for the time interval two to three second and the time interval three to four second. So what do we observe? We observe that equal amount of distances are travelled in equal intervals of time. So we see that equal distance is covered in equal intervals of time. We know that distance divided by time gives us the speed. So distance by time is speed and what can we say for this? That speed in this time interval is equal to the speed in this time interval. And same in this time interval and this time interval. So we conclude that the boy is moving with uniform speed. That is his speed is not changing while he moves. Now observe this again. He covers ten meters in the first second. In the second second, this time he covers thirty meters. In the third second, he covers ten meter that is forty to fifty is ten. In the fourth second, he went from fifty to seventy and hence he covered twenty meters. So we get this table for representing the motion of the boy. In time interval zero to one second he took one second to travel a distance of ten meters. In time interval one to two second he again took one second but this one second he travelled a distance of thirty meters. In time interval of two to three second he took one second but this time he travelled ten meters. In three to four second, he travelled twenty meters. So we see that unequal distance is covered in equal intervals of time. So unequal distance ten thirty ten twenty covered in equal intervals of time. Time interval remains the same that is one and again we know that distance by time is speed. So this time speed in this interval is not the same as that of speed in this interval. So we can say that the boy is moving with non-uniform or variable speed. That is his speed varies as he moves and it is not constant throughout the journey. Now we observe the motion of this boy again and we keep direction in mind this time. So he moves ten meters towards right in the first second. Another ten meters towards right in the second second. Again ten meters towards right in the third second. And ten meters towards right in the fourth second. Now since we are mentioning direction over here means we are measuring the displacement of boy. So in the time interval zero to one second, time taken is one second and displacement is plus ten meters. So we have taken the rightward direction as the positive direction, so displacement of ten meters towards right becomes the displacement a plus ten meters. So in one to two second, we remember he travelled ten meters towards right. So the displacement again is plus ten meters. same for two to three seconds displacement was plus ten in one second. three to four second, displacement was Plus ten in one second. So what do we observe here? We observe that equal distances is covered in equal intervals of time along the same direction. So equal distance that is a distance of ten meters is covered in equal intervals of time. Equal intervals of time here is one second along the same direction. So the direction is the same that is displacement is always in the positive direction and displacement by time gives us velocity. So we say that velocity is the same for each time interval. Hence we conclude that the boy is moving with uniform velocity and when something is moving with uniform velocity it is said to be in uniform motion. So the boy is moving with uniform velocity that is with a constant velocity throughout the journey. Now let us observe the motion of this boy again. He travels ten meters towards right in the first second. Again from then ten meters to forty meters that is thirty meters towards right in the second second. From forty to fifty, he travels ten meters towards right in the third second and twenty meters towards right in the fourth second. So this table shows the displacement of boy along different time intervals. In time interval zero to one Second, the time taken is one second. The displacement of the boy was plus ten meters again here also we have considered the rightward direction as the positive direction. So displacement towards right have been denoted by plus sign. So it is plus ten meters. Time interval one to two second, time taken is one second and the displacement is plus thirty meters. In two to three second, the displacement is plus ten meters and in three to four seconds, the displacement is plus twenty meters. So what do you observe here? Here we observe that the direction is always positive that is as we had seen also in the video boy always has travelled in rightward direction. So the direction of displacement is the same. However the magnitude of displacement varies. That is in this case the magnitude of displacement is ten. In this case the magnitude of displacement is thirty. Here it is ten and here it is twenty. So different amount of displacement takes place in equal intervals of time or we say that unequal distance is covered in equal intervals of time along the same direction and the boy is said to be moving with non-uniform velocity. So the boy here is moving with non-uniform velocity or he is in non-uniform motion. Now let us see one more case. The boy moves ten meters towards right in the first second. In the second second, he moves ten meters towards right. He turns and moves towards left ten meters in the third second. He again turns and moves ten meters towards right in the fourth second. So this is what we have. In time interval zero to one second, the time taken is one second and the displacement of boy is plus ten meters because he travelled in the rightward direction. In time interval, one to two second the displacement of boy was ten meters because again he travelled in the rightward direction and time interval two to three second, the displacement was minus ten meters. Why? Because if rightward direction is the positive what will be the minus direction? The leftward direction and in two to three second, the boy moves ten meters towards left. So his displacement is minus ten meters. In three to four second, the boy moves ten meters towards right and his displacement is plus ten meters. So we see that equal distance is covered in equal intervals of time but the direction changes. So we see that the magnitude of displacement is the same in this case. Magnitude of displacement is ten in all the four intervals but the direction is right sometimes. It is to the left sometimes and hence the velocity is different for each time interval. And we see the boy is moving with non-uniform velocity So when is a body said to be in non-uniform velocity? Well A body is set to be in non-uniform motion or it is said to be travelling with non-uniform velocity if it travels unequal distances in same direction in equal intervals of time that is the magnitude of displacement changes but the direction does not change or it changes its direction of motion or both. So what have we learnt? We have learnt that when a body covers equal distances in equal intervals of time it is said to be moving with uniform speed. When a body covers unequal distances in equal intervals of time, it is said to be moving with non-uniform speed. When a body has equal displacement in equal intervals of time it is said to be moving with
non with uniform velocity or in uniform motion and when a body covers either unequal distances in equal intervals of time or changes its direction of motion in equal intervals of time then it is said to be moving with non-uniform velocity or it is said to be non-uniform motion.

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