Motion In a Straight Line - 11th physics

When an object moves from one place or point to other place or point, it is said that the object is in motion. For example falling of leaves from a tree, blowing of air, running of a dog, running of a boy, flying of a bee, running of a vehicle, etc.

In the universe everything is moving whether, it is a start or a meteor. Our earth is moving round the sun, moon is moving round the earth, even sun is moving in the galaxy.

Definition of Motion: Motion is change in position of an object with time. This means when an object changes its position with lapse of time, that very object is said to be in motion.

Rectilinear Motion

The motion of an object along a straight line is known as Rectilinear Motion. For example motion of a cyclist along a straight road.

While considering the motion the object is considered as a point size.

Kinematics

Kinematics is a branch of physics in which the motion of an object is studied without considering the cause of motion.

Position, Path Length and Displacement

To consider motion of an object four things are required. These are position of the object, path length of the object through which it moves, displacement of the object and time.

Position of the Object

Positions of an object while its motion a reference point and a set of axes are needed to be kept in observation.

Conventionally, a rectangular coordinate system consisting three mutually perpendicular axes, labeled X-axis, Y-axis and Z-axis are chosen as axes.

Origin of the movement of the object

The point of intersection of axes is chosen as reference point. The intersection of axes is known as Origin (O). The origin is generally denoted by English letter "O".

Frame of Reference

The rectangular coordinate system consisting three mutually perpendicular axes, labeled X-axis, Y-axis and Z-axis are chosen as axes along with a clock constitutes a frame of reference.

For rectilinear motion only one axis is considered. Usually, X-axis only is considered for motion of an object in straight line.

Object in Motion and Object in Rest

If an object changes its position along with one or more coordinates with time, object is said to be in motion otherwise object is said to be at rest with respect to the frame of reference.

Path Length – Distance

The total length covered by an object while in motion is called Path Length.

Example

Case – (i)

Let a car starts from point O. This car goes to C along point A and B.

Thus, Length of path covered by car (OC) = OA + AB + BC

Let OA = 10 m, AB = BC = 15 m

Thus, Total Length of path (OC) = 10m + 15m + 15m

⇒ OC = 40m

Case – (ii)

Let a car starts from point O and goes to point C and return to point A.

Thus, path length = OC + CA

Let OA = 10 m, AB = BC = 15 m

Thus, OC = 40 m and CA = 30 m

Thus, OC + CA = 40m + 30m

⇒ OC + CA = 70m

Thus, path length = 70m

Negative and Positive Measurement of Path Length

Conventionally, Origin point O is considered as 0

And, right to the origin point is considered positive and left to the origin point is considered as negative measurement.

Displacement

The change in position of an object in motion is called the Displacement.

Let x₁ is the position of an object at time t₁.

And x₂ is the position of that object at time t₂.

Thus, change in time

The change is denoted by Δ (A Greek Letter)

Thus, the change in time is denoted by Δt

Thus, The displacement, i.e. change in position is given by the difference between the final and initial position

Displacement (change in position) is denoted by Δx

Thus,

Thus, displacement (Δx) in the change in time (Δt) = x₂ – x₁

Example

Case – (i)

Let a car starts from point O and goes to point C and return to point A.

Thus, path length = OC + CA

Let OA = 10 m, AB = BC = 15 m

Thus, OC = 40 m and CA = 30 m

Thus, OC + CA = 40m + 30m

⇒ OC + CA = 70m

Thus, path length = 70m

And Displcement = Change in Position = OA

Here, since, OA = 10m

Thus, Displacement = 10m

Vectors and Scalars Quantities

Quantities which has both magnitude and direction are known as Vector quantities. And quantities those have only magnitude and no direction are known as Scalar quantities.

Displacement has both magnitude and direction. Thus, Displacement is a Vector quantity.

Positive and Negative Displacement

If x₁ is smaller than that of x₂, then displacement is considered as positive. And if x₁ is greater than that of x₂, then displacement is considered as positive.

Zero Displacement

Case – (ii)

Let a car starts from point O and goes to point C and return to point O.

Thus, path length = OC + OC

Let OA = 10 m, AB = BC = 15 m

Thus, OC = 40 m

Thus, OC + OC = 40m + 40m

⇒ OC + OC = 80m

Thus, path length = 70m

And, Displacement = 0

Since, car returns to its initial position.

Thus, the magnitude of displacement for a course of motion may be zero but the corresponding path length is not zero.

The magnitude of displacement may or may not be equal to the path length traversed by an object.

Position–Time Graph

Motion of an object can be represented by a position–time graph. Such graph is a very good and powerful tool to represent and analyse different aspects of motion of an object.

For motion along a straight line only X-coordinate varies with time. Such graph is called x-t graph also.

Position-Time graph (a) says that object is still at 40m continuously. This means object is at rest. As the Position-Time graph is straight line and parallel to time-axis.