**The Course Designed based on the pattern of NCERT.Useful and advanced content are added as per Edusaint's Learning framework to enable the student to prepare for IIT foundation and other Relevant exams.**

**UNIFORM AND NON-UNIFORM MOTION**

- A body has a
**uniform motion**if it travels equal distances in equal intervals of time, no matter how small these time intervals may be. - For example, a car running at a constant speed of say, 20 metres per second, will cover equal distances of 20 metres, every second, so its motion will be uniform.

The distance-time graph for uniform motion in a straight line.

A body has a non-uniform motion if it travels unequal distances in equal intervals of time.

- For example, if we drop a ball from the roof of a tall building, we will find that it covers unequal distances in equal intervals of time. It covers :
- 3.9 metres in the 1st second,
- 12.7 metres in the 2nd second,
- 22.5 metres in the 3rd second, and so on.
- Thus, a freely falling ball covers smaller distances in the initial ‘1-second’ intervals and larger distances in the later ‘1 second’ intervals.

**The motion of a train starting from the Railway station**is also an example of non-uniform motion.- This is because when the train starts from a Station, it moves a very small distance in the ‘first’ second.
- The train moves a little more distance in the ‘2nd’ second, and so on.

- And when the train approaches the next Station, the distance travelled by it per second decreases.
- Please note that the distance-time graph for a body having non-uniform motion is a curved line.

**SPEED AND VELOCITY**

- Although
**speed and velocity**are often used interchangeably in everyday life, they represent different quantities in physics.

What is speed?

- Speed is a measurement of how fast an object moves relative to a reference point.
- It does not have a direction and is considered a magnitude or scalar quantity.
- Speed can be figured by the formula:
**Speed = Distance/Time****or****s = d/t**

**The measurement of speed can reflect two different scalar quantities.**

**Instantaneous Speed**– The speed of an object at a given moment.- The car may be travelling at 50 mph at this moment, but it may slow down or speed up during the next hour.
**Average Speed –**The average speed is calculated by the distance that an object travelled over a given interval of time.- If a car travelling 50 miles over the course of one hour then its average speed will be 50 mph.
- It may be that the car travelled at instantaneous speeds of 40 mph and 60 mph during that time, but the average speed is 50 mph.

**Average Speed **

- The average speed of a body is the total distance travelled divided by the total time taken to cover this distance.
- While travelling in a car (or a bus) we have noticed that it is very difficult to keep the speed of the car at a constant or uniform value because at many places the brakes are to be applied to slow down or stop the car due to various reasons.
- Thus, the speed of a body is usually not constant and the distance travelled divided by time gives us the average speed during that time.
- For example, for a car which travels a distance of 100 km in 4 hours, the average speed is 100/4= 25 km per hour.
- Although the average speed of this car is 25 km per hour, it does not mean that the car is moving at this speed all the time.
- When the road is straight, flat and free, the speed may be much more than 25 km per hour but on bends (curved road), hills or in a crowded area, the speed may fall well below this average value. We should remember that :

Average speed = Total distance/ Total time taken

**Uniform Speed (or Constant Speed)**

- A body has a uniform speed if it travels equal distances in equal intervals of time, no matter how small these time intervals may be.
- For example, a car is said to have uniform speed of say, 60 km per hour, if it travels 30 km every half hour, 15 km every quarter of an hour, 1 km every minute, and 160 km every second.
- As we have already discussed above, in actual practice the speed of a body rarely remains uniform (or constant) for a long time.
- If, however, the speed of a body is known to be constant, we can find out exactly how much distance it will travel in a given time or if we know the distance travelled by the body, we can calculate the time taken to travel that distance. We will now solve some numerical problems based on speed.

**Sample problem**

**Problem**. A scooterist covers a distance of 3 kilometres in 5 minutes. Calculate his speed in :

(a) centimetres per second (cm/s)

(b) metres per second (m/s)

(c) kilometres per hour (km/h)

Solution. (a) In order to calculate the speed in centimetres per second we should convert the given distance of 3 kilometres into centimetres and the given time of 5 minutes into seconds. Please note that 1 kilometre has 1000 metres and 1 metre has 100 centimetres. Now,

Distance travelled =3 km = 3 × 1000 m = 3 × 1000 × 100 cm = 300,000 cm …. (1)

Time taken = 5 minutes = 5 × 60 seconds = 300 s …. (2)

We know that, Speed = Distance travelled /Time taken = 300,000 cm /300 s= 1000 cm/s …. (3)

Thus, the speed of scooterist is 1000 centimetres per second.

(b) In order to express the speed in metres per second we should convert the given distance of 3 kilometres into metres and the given time of 5 minutes into seconds. Thus, in this case :

Distance travelled =3 km = 3 × 1000 m = 3000m

Time taken = 5 minutes = 5 × 60 seconds = 300 s …. (5)

Now, Speed = Distance travelled /Time taken = 3000 m/ 300 s = 10 m/s …. (6)

So, the speed of scooterist is 10 metres per second.

(c) And finally, in order to calculate the speed in kilometres per hour, we should express the given distance in kilometres (which is already so), and the given time in hours. So, in this case :

Distance travelled = 3 km …. (7)

Time taken = 5 minutes = 5/60 hours = 0.083 h …. (8)

We know that Speed = Distance travelled /Time taken = 36 km/h …. (9)

Thus, the speed of scooterist is 36 kilometres per hour.