**Important Notes on Motion Class 9 – Chapter-8**

**Position**

The location of an object with respect to a particular point, is known as the position of the object.

**Scalar and Vector quantities**

Physical quantities with which we can associate only magnitude, i.e. numbers are called scalar quantities. e.g. time, mass, speed, distance etc.

Physical quantities with which we can associate magnitude, i.e. numbers as well as direction are called vector quantities.

**Distance versus Displacement**

1. Displacement of a moving object can never be greater than the distance travelled by it.

2. If a body moves along a straight line (only in one direction), then distance and displacement will be equal.

3. The magnitude of the displacement for a course of motion may be zero but the corresponding distance covered is not zero.

4. Displacement of the object can be positive, negative or zero.

**Example:** A jogger jogs along one length and breadth of a rectangular park. If the dimensions of park are 150m × 120m, then find the distance travelled and displacement of the jogger.

**Solution: **According to question

Length, l= 150m, Breadth, b= 120m

Distance travelled, s= ?

Displacement of the jogger= ?

Suppose, the jogger starts from point A and after covering one breadth and one length reaches at point C.

Distance, s = Length of the total path covered= AB + BC

S = 150 + 120= 270m

Thus, the jogger travels a distance of 270m and his displacement is 30√41m.

**Uniform and non-uniform motion**

**Uniform motion**

A body is said to have a uniform motion, if it travels equal distances in equal intervals of time.

**Non-uniform motion**

A body is said to have a non-uniform motion, if it travels unequal distances in equal intervals of time.

**Rate of motion**

The ratio of distance travelled by an object and time taken is called rate of motion.

**Speed**

Speed of an object is defined as the distance travelled by it in per unit time.

Speed of an object (v) = Distance/Time

Speed is a scalar quantity. The SI unit of speed is metre per second (m/s).

**Types of speed**

The various types of speed are as given below:

**(i) Uniform speed: **If a moving body covers equal distances in equal intervals of time, then the speed of the body is said to be uniform, i.e. constant speed.

**(ii) Non-uniform speed:** If a moving body covers unequal distances in equal intervals of time, then the speed of the body is said to be non-uniform, i.e. variable speed.

**(iii) Average speed:** It is defined as the ratio of the total distance travelled by a body to the total time taken. It is expressed as

Average speed = Total distance travelled/ Total time taken

= s_{1} + s_{2} + s_{3} +…/ t_{1} + t_{2} + t_{3} +…

**(iv) Instantaneous speed: **The speed of an object at any particular instant of time or at a particular point of its path is called the instantaneous speed of the object.

**Example:** An object travels 14m in 4s and then another 16m in 2s. What is the average speed of an object?

**Solution:** According to question, First distance, s_{1} = 14m

Second distance, s_{2} = 16m, Times, t_{1} = 4s, t_{2} = 2s

∴ Average speed= Total Distance/Total Time = s1 + s2 / t1 + t2

=14+16/4+2

=30/6

= 5m/s

Therefore, the average speed of an object is 5m/s.

**Speed with direction : Velocity**

Velocity of an object (v) = Displacement (d) / Time (t)

Velocity is a vector quantity. The SI unit of velocity is metre per second (m/s). Velocity of an object can be positive, zero or negative.

**Types of velocity**

The various types of velocity are as given below:

**(i) Uniform velocity: **If an object covers equal displacements in equal intervals of time without changing direction, then its velocity is known as uniform velocity, i.e. constant velocity.

**(ii) Non-uniform velocity:** If an object covers unequal displacements in equal intervals of time, then its velocity is known as non-uniform velocity, i.e. variable velocity.

**(iii) Average Velocity: **It is defined as the ratio of total displacement of the object to the total time taken.

It is expressed as

V_{av} = Total displacement / Total time taken

If the velocity of an object changes at a uniform rate, then average velocity,

(v_{av}) = u + v / 2

**(iv) Instantaneous velocity: **The velocity of an object at a particular instant of time or at a particular point of its path is called its instantaneous velocity.

**Example:** Rajeev went from Delhi to Chandigarh on his motorbike. The odometer of that read 4200 km at the start of trip and 4460 km at the end of his trip. If Rajeev took 4h 20min to complete his trip, then find the average speed and average velocity in km/h as well as in m/s.

**Graphical representation of motion**

**Types of graph**

**1. Distance-time graph**

The change in the position of an object with time can be represented on the distance-time graph adopting a convenient scale of choice.

**(i) Distance-time graph for uniform motion**

If an object travels equal distances in equal intervals of time, then it moves with uniform speed.

**(ii) Distance-time graph for non-uniform motion**

It a body travels unequal distances in equal intervals of time, then the motion of the body is known as non-uniform motion.

**2. Velocity-Time graph**

**(i) Velocity-Time graph for a body moving with constant velocity**

**(ii) Velocity-Time graph for uniform accelerated motion**

**(iii) Velocity-Time graph for non-uniform accelerated motion**

Try to Answer These Questions

**Q1. Three Difference between Distance and Displacement.**

**Q2. Types of velocity. Explain briefly.**

**Q3. An object travels 14m in 4s and then another 16m in 2s. What is the average speed of an object?**