ICSE Class 9 Physics Chapter 02 Motion in One Dimension

Motion In One Dimension

Syllabus

Scalar and vector quantities, distance, speed, velocity, acceleration; graphs of distance-time and speed-time. Equations of uniformly accelerated motion with derivations.

Scope - Examples of scalar and vector quantities only, rest and motion in one dimension, distance and displacement, speed and velocity, acceleration and retardation, distance-time and velocity-time graphs; meaning of slope of the graphs. (Non-uniform acceleration excluded). Equations to be derived: \(v = u + at\); \(S = ut + \frac{1}{2}at^2\); \(S = \frac{1}{2}(u + v)t\); \(v^2 = u^2 + 2aS\) (equation for \(S_n^{th}\) is not included). Simple numerical problems.

Some Terms Related To Motion

Scalar And Vector Quantities

The quantities which we can measure are called the physical quantities. The physical quantities are classified into the following two broad categories: (1) Scalar quantities or scalars, and (2) Vector quantities or vectors.

Scalar quantities or scalars: These are the physical quantities which are expressed only by their magnitude. For example, if we say that the mass of a body is 5.0 kg, it has a complete meaning and we are completely expressing the mass of the body. Thus, we need the following two parameters to express a scalar quantity completely:

(i) Unit in which the quantity is being measured, and

(ii) The numerical value of the quantity.

Remember that if the scalar is a pure number (like \(\pi\), \(e^2\), etc.), it will have no unit.

Examples: Mass, length, time, distance, density, volume, speed, temperature, potential (gravitational, magnetic and electric), work, energy, power, pressure, quantity of heat, specific heat, charge, electric power, resistance, density, mechanical advantage, frequency, angle etc.

Scalar quantities can be added, subtracted, multiplied and divided by the simple arithmetic methods. Scalar quantity is symbolically written by its English letter. For example, mass is represented by the letter m, time by t and speed by v.

Vector quantities or vectors: These physical quantities require the magnitude as well as the direction to express them, then only their meaning is complete. For example, if we say that "displace a particle from a point by 5 m", the first question that will arise, will be "in which direction"? Obviously, by saying that the displacement is 5 m, its meaning is incomplete. But if we say that displace the particle from that point by 5 metre towards east (or in any other direction), it has a complete meaning. Thus, we require the following three meters to express a vector quantity completely:

(i) Unit,

(ii) Numerical value of the quantity and

(iii) Direction.

Examples: Displacement, velocity, acceleration, momentum, force, moment of a force (or torque), impulse, weight, temperature gradient, electric field, magnetic field, dipole moment, etc.

The numerical value of a vector quantity alongwith its unit gives us the magnitude of that quantity. It is always positive. The negative sign with a vector quantity implies the reverse (or opposite) direction. Vector quantities follow different algebra for their addition, subtraction and multiplication. A vector quantity is generally written by its English letter bearing an arrow on it or by the bold English letter. For example, velocity is written as \(\vec{v}\) or v, acceleration by \(\vec{a}\) or a, force by \(\vec{F}\) or F. Obviously the forces \(\vec{F}\) and \(-\vec{F}\) are in opposite directions.

Rest And Motion

Every object in the universe is in motion. Everyday we see bodies moving around us e.g. birds flying, cars and buses moving, people walking, insects crawling, animals running etc. Our earth also moves around the sun so every thing on it is in a state of motion. The sun and stars are moving around the centre of their galaxy and the galaxies too are not at rest.

Although nothing is at rest, but we often say that a stone lying on the ground is at rest because the stone does not change its position with respect to us. Similarly, if we are sitting on a railway platform and look at a tree nearby, we say that the tree is at rest because it does not change its position with respect to us. But when we see a train leaving the station, we say that the train is in motion because it is continuously changing its position with respect to us. Thus,

A body is said to be at rest if it does not change its position with respect to its immediate surroundings, while a body is said to be in motion if it changes its position with respect to its immediate surroundings.

For a moving body, if the distance travelled in a certain time interval is much large as compared to the size of the body, the body can be assumed to be a point particle. In this chapter, we shall study the description of motion of a body assuming it to be a point particle.

One dimensional motion: When a body moves along a straight line path, its motion is said to be one dimensional motion. It is also called motion in a straight line or rectilinear motion. For example, the motion of a train on a straight track, a stone falling down vertically, a car moving on a long and straight road etc., are one dimensional (or rectilinear) motions. In such a motion, there is no movement of the body in lateral direction (i.e., no sideways motion).

If a body moves on a plane along a curved path, its motion is two dimensional and if it moves in space, its motion is three dimensional. In this chapter, we shall consider only the one dimensional motion.

Representation of one dimensional motion: The path of one dimensional motion can be represented by a straight line parallel to the X-axis if X-axis is taken in the direction of motion. Each point on the straight line represents the position of particle at different instants. The position of particle at any instant t is expressed by specifying the x coordinate at that instant. As the particle moves, its x coordinate will change with time t.

Example: The position of a pebble measured from its starting point, falling freely and vertically downwards at different instants is given in the table below:

The motion of the pebble can be represented by choosing a proper scale for x on a straight line along X-axis as shown in Fig. 2.1. Here X-axis represents the vertically downward direction.

\(x = 0\) 5 m (at t = 0) 20 m (at t = 1 s) 45 m (at t = 2 s) 80 m (at t = 3 s) (at t = 4 s)

Distance And Displacement

Consider a body moving from a point A to a point B along the path shown in Fig. 2.2. Then total length of path from A to B is called the distance moved by the body, while the length of straight line AB in direction from A to B (shown by the dotted line in Fig. 2.2) is called the displacement of the body.

Distance

The total length of path through which a body moves, is called the distance travelled by it. The distance travelled by a body depends on the path followed by the body.

It is a scalar quantity. It is generally represented by the letter S.

Unit: The S.I. unit of distance is metre (m) and C.G.S. unit is centimetre (cm).

Displacement

The shortest distance from the initial to the final position of the body, is the magnitude of displacement and its direction is from the initial position to the final position.

It is a vector quantity. It is represented by the symbol \(\vec{S}\).

Unit: The S.I. unit of displacement is metre (m) and C.G.S. unit is centimetre (cm).

Teacher's Note

When you walk from home to school, the actual path distance is the distance traveled, but the straight-line path from home to school is your displacement. This difference is crucial in physics for understanding motion.

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