No More Mistakes With Motion in Straight Line class 11th Part 2

DoubtConnect
5 min readJul 6, 2022

For a better understanding of the concept, we would recommend that you check out the first part of this blog as well. Give it a quick read and once you are done, hop on to this one to ace the concept.

During Part 1, we discussed the concept of motion in which objects are positioned differently over time. In mathematics, motion is defined as displacement, distance, velocity, speed, acceleration, and time. Motion can be evaluated by attaching a frame of reference to a body. The motion is assessed based on the change in position of the body relative to the frame.

Throughout this explainer, we’ll learn that distance is the distance between two points, while displacement represents the distance between those two points in straight lines.

Let’s begin by talking about distance

Whenever an object travels from one point to another, it is moving along a path connecting those points. Every path a traveling object takes has a length. The length represents the distance taken by the object on that path.

It is possible for two points to be connected by a straight line. In the figure below, an object can be seen following a straight path.

As illustrated in the following figure, a path can also be curved between two points.

The distance traveled by an object doesn’t differ from straight lines and curves regardless of where it originates or where it ends. This is because in either case, the length of the line is the same. In other words, distance has no direction, only magnitude.

The type of quantity that has a magnitude but no direction is a scalar quantity; as a result, distance is also a scalar quantity.

If an object moves, the motion may occur between several points.

Here is an illustration showing how an object moves from point A to point B, then from point B to point C.

A movement from A to B and a movement from B to C can be described as the movement of the object.

The distance, 𝑑, that the object travels is given by 𝑑= (distance from A to B) + (distance from B to C)

Under distance comes,

  • Speed
  • Average speed

SPEED

In linear motion, an object travels along a straight path at a constant speed. In other words, it is the distance an object travels in a given amount of time. A meter per second (m/s) is the unit for linear speed.

Average Speed

In a time interval during which the motion took place, the average speed is calculated by dividing the total path length by the total interval during which it took place:

Total path length = Average speed Total time interval

It should be noted that average speed and velocity have the same unit (m s–1). Unfortunately, that doesn’t tell us in which direction the object is moving. Thus, it is always positive.

Moving on to displacement

In addition to changing position, objects also have displacement when they move a distance.

As another measure of distance, displacement also describes how far points are separated from one another, but it is not the same as distance.

Displacement differs from a distance because displacement has a direction. It is a vector quantity when it has both a direction and magnitude, so displacement is a vector quantity. Displacement is commonly denoted by the symbol ‘s’.

The following figure shows a line drawing connecting the two points in displacement.

Further, under this, we will study velocity and Average Velocity

Velocity

Particles moving in a straight line have an average velocity of zero in an interval. Velocity is a vector quantity.

Average Velocity

The position of an object changes over time when it is in motion. However, how fast does the position change, and in what direction? We can describe this through the term average velocity. An average velocity is a difference between the position or displacement change (∆x) dividing the time interval (∆t), in which the displacement occurred:

It depends on the sign of the displacement whether the average velocity is positive or negative. If there is no displacement, the average velocity is 0. In the following diagrams, several x-t plots are shown. The diagrams show an object at rest, moving at a positive velocity, and moving at a negative velocity.

Instantaneous Speed and Instantaneous velocity:

For a very short period of time (almost zero), the instantaneous velocity is the rate at which the position of an object changes. Using m/s as a measurement unit. The instantaneous speed is defined as the magnitude of the instantaneous speed. Its value is the same as that of instantaneous velocity, but its direction is not specified.

KEY POINTS

  • A positive displacement is taken into account for motion along a line by picking a direction from one end of the line to the other. A negative displacement is taken into account for motion in the opposite direction.
  • The distance between two points along a straight-line path is equal to the displacement along that path.
  • Zero displacements are produced when an object travels from a point back to that same point.

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