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### What is Motion?

**Motion Class 9 Notes –** Motion is the change in an object’s position with relation to its environment over time. Velocity, acceleration, and displacement are only a few examples of the different physical quantities that can be used to characterise motion.

**Velocity:**The speed of an object in a specific direction is known as its velocity.. It is a vector quantity that tells us how fast an object is moving and in what direction. For example, a car moving at 60 miles per hour north has a velocity of 60 mph north.**Acceleration:**The rate at which an object’s velocity changes over time is known as acceleration. It is a vector quantity that tells us how quickly an object’s velocity is changing and in what direction. For example, a car accelerating from 0 to 60 miles per hour in 5 seconds has an acceleration of 12 mph/s.**Displacement:**Displacement is the change in an object’s position from its starting point to its ending point, measured in a straight line. It is a vector quantity that tells us how far an object has moved and in what direction. For example, if you walk from your house to the store and back, your displacement is the straight-line distance between your house and the store.

## Motion Class 9 Notes

#### Distance and Displacement

Distance and displacement are both measures of the motion of an object, but they are different concepts. Distance is a scalar quantity that refers to the total path length traveled by an object, while displacement is a vector quantity that refers to the change in position of an object from its starting point to its ending point, measured in a straight line.

#### Uniform motion and Non-uniform motion

**Uniform Motion – **An object is said to be in uniform motion when it moves in a straight path at a constant speed. For example, if a car is moving from one place to another place at a constant speed of 31.25 Km/h on the straight line it means that the car is moving with uniform motion.

**Non-uniform Motion – **Non-uniform motion is the movement of an object in a straight line with varied rates. For example, if car moving from one place to another place and the car speed is increasing and decreasing depend on the road it means that motion is non-uniform manner.

#### Time and Speed

Time and speed are two concepts that are closely related in physics and mathematics. Speed is a measure of how quickly an object moves, and is typically measured in units of distance per unit time, such as meters per second (m/s) or miles per hour (mph). Time, on the other hand, is a measure of duration or elapsed time, and is typically measured in units of seconds, minutes, hours, or other time units.

The relationship between time and speed can be expressed mathematically using the formula:

speed = distance / time

This formula tells us that the speed of an object is equal to the distance it travels divided by the time it takes to travel that distance. For example, if a car travels 100 kilometers in 2 hours, its average speed is 50 kilometers per hour (km/h).

Similarly, we can also use the formula to calculate the time it takes for an object to travel a certain distance at a given speed. For example, if a train is traveling at a speed of 80 km/h and needs to travel a distance of 240 km, we can calculate the time it will take by rearranging the formula as follows:

time = distance / speed

240 km / 80 km/h = 3 hours

So, the train will take 3 hours to travel the distance of 240 kilometers if it maintains a constant speed of 80 kilometers per hour.

##### Average Speed

Average speed is calculated by dividing the total distance travelled by an object by the total amount of time needed to cover that distance.

The formula for calculating average speed is:

Average speed = Total distance traveled / Total time taken

For example, if a car travels 200 kilometers in 4 hours, its average speed would be:

Average speed = 200 km / 4 hours = 50 km/h

This means that the car traveled an average of 50 kilometers per hour over the 4-hour period.

#### What is Velocity?

Velocity is a vector quantity that describes both the speed and direction of motion of an object. It is defined as the rate of change of an object’s position with respect to time, in a specific direction. The direction of velocity is important, because two objects can have the same speed but different velocities if they are moving in different directions.

The formula for calculating velocity is:

Velocity = Displacement / Time

where displacement is the change in an object’s position, and time is the duration over which the displacement occurs. The displacement is a vector quantity that describes the distance and direction between an object’s starting and ending points.

For example, if a car moves from one point to another point 50 kilometers away in 2 hours, and its displacement is also 50 kilometers (in the direction of its motion), then its velocity can be calculated as:

Velocity = Displacement / Time

50 km / 2 hours = 25 km/h

The velocity of the car is 25 kilometers per hour in the direction of its motion.

#### Acceleration

The rate at which an object’s velocity changes over time is called its acceleration. It is a vector quantity that describes both the magnitude and direction of the change in velocity.

The formula for acceleration is:

Acceleration = Change in Velocity / Time

where the change in velocity is the difference between an object’s final velocity and its initial velocity, and time is the duration over which the change in velocity occurs.

If the change in velocity is in the same direction as the initial velocity, the acceleration is called positive. If the change in velocity is in the opposite direction to the initial velocity, the acceleration is called negative, or deceleration.

For example, if a car starts from rest and reaches a velocity of 50 km/h in 10 seconds, its acceleration can be calculated as:

Acceleration = (50 km/h – 0 km/h) / 10 s = 5 km/h/s

The acceleration of the car is 5 kilometers per hour per second, in the direction of its motion.

It’s important to note that acceleration can also occur if an object is moving in a curved path, even if its speed is constant. This is because the direction of motion is changing, which means that the velocity is also changing, and therefore the object is accelerating. This is known as centripetal acceleration.

### Graphical representation of motions

#### Distance-time graph

A distance-time graph is a graph that shows the distance an object has traveled as a function of time. The distance is plotted on the y-axis, and the time is plotted on the x-axis.

#### Velocity-time graph

A velocity-time graph is a graphical representation of an object’s velocity over a period of time. The graph plots the object’s velocity on the y-axis and time on the x-axis.

##### (i) Velocity-time relation

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.