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Understanding Physics Topics is essential for solving complex problems in many fields, including engineering and medicine.

## Explain about Motion and Fast and Slow Moving Objects

The movement of an object is called motion. The moment (or duration) in which things occur is called time. An object is said to be in motion (or moving) when its position changes with time. For example, when the position of a car changes with time, we say that the car is moving or that the car is in motion.

The motion (or movements) of all the objects are not of the same type. Different objects show different types of motion (or movements). In Class VI we have learnt that there are four important types of motion: Rectilinear motion, Circular motion, Rotational motion, and Periodic motion.

1. Rectilinear Motion.

Motion in a straight line is called rectilinear motion. In other words, when an object moves along a straight line path, it is called rectilinear motion. The motion of a bullock cart moving on a straight road is rectilinear motion (or motion along a straight line). Some other examples of rectilinear motion (which takes place along a straight line) are : Motion of a horse pulling a cart on a straight road ; Motion of a train on a straight bridge; and March past of soldiers in a parade.

2. Circular Motion.

A round path having the shape of a circle is called circular path. When an object moves along a circular path, it is called circular motion. For example, the earth moves around the sun in a circular path (or circular orbit), so the motion of the earth around the sun is circular motion. Some other examples of circular motion are : Motion of a child in a merry-go-round; and Motion of pedals of a moving bicycle.

3. Rotational Motion.

When an object turns (or spins) about a fixed axis, it is called rotational motion. The earth turns round and round on its axis like a spinning top, so the spinning of earth on its axis is an example of rotational motion. The turning of the blades of a fan also represents rotational motion.

4. Periodic Motion.

The motion which repeats itself after regular intervals of time, is called periodic motion. Periodic motion is also called oscillatory motion. The swinging of a pendulum is an example of periodic motion (or oscillatory motion). Some other examples of the periodic motion are : Motion of a swing (or jhoola) ; Motion of hands of an athlete while running a race ; Motion of a child on a see¬saw ; and Motion of hammer in an electric bell.

The simplest of all types of motion is the rectilinear motion (commonly called ‘linear motion’) which takes place along a straight line path (like a straight road). We will now describe the linear motion of objects in terms of speed.

### Slow And Fast Moving Objects

It is a common experience that the motion of some objects is slow whereas that of other objects is fast. This point will become clear from the following example. Suppose our school is at’ a distance of 4 kilometres from our home. If we go to school by bicycle, it may take about 20 minutes time to cover the distance of 4 kilometres and reach the school.

On the other hand, if we go to school by school bus, the same distance of 4 kilometres can be covered in say, only 5 minutes. This means that a bicycle takes a longer time (20 minutes) to cover a distance of 4 kilometres whereas a bus takes a much shorter time (5 minutes) to cover the same distance of 4 kilometres.

We say that a bicycle moves slow whereas a bus moves fast. In other words, a bus moves faster than a bicycle. Even the same object may move slow at one time and fast at other times. For example, the same bus will move slow when the road is congested with lot of traffic and move fast when the road is free.

From the above discussion we conclude that an object which takes a longer time to cover a certain distance is called slow whereas another object which takes a shorter time to cover the same distance is said to be fast. The most convenient way to find out which of the two objects is moving faster is to compare the distances moved by them in a unit time (say, in ‘one hour’, in ‘one minute’ or in ‘one second’).

The distance moved by an object in a unit time is called speed of the object. This means that we can find out whether an object is slow or fast by knowing its speed. A slow moving object is said to have a low speed. On the other hand, a fast moving object is said to have high speed. A higher speed indicates that a given distance has been covered in a shorter time. We will now discuss the speed of objects (like scooters, motorcycles, cars, buses, trucks, etc.) moving along a straight line path in detail.

### Speed

If a car runs slow, we say that its speed is low and if a car runs fast, we say that its speed is high. Thus, the speed of an object (like a car) gives us an idea of how slow or fast that object is moving. We can define the speed of a moving object as follows : Speed of an object is the distance travelled by it in unit time. The speed of an object can be calculated by dividing the ‘distance travelled’ by the object, by the ‘time taken to travel this distance. The formula for calculating the speed of an object is:

Speed = \(\frac{\text { Distance travelled }}{\text { Time taken }}\)

Suppose a car travels a distance of 100 kilometres in 4 hours. Then the speed of this car is given by:

Speed = \(\frac{100 \text { kilometres }}{4 \text { hours }}\)

Speed = 25 kilometres per hour

**Example Problem 1.**

A man riding a scooter travels a distance of 50 metres in 20 seconds. What is the speed of the scooter ?

**Solution:**

The formula for calculating speed is:

Speed = \(\frac{\text { Distance travelled }}{\text { Time taken }}\)

Here, Distance travelled = 50 m

And, Time taken = 20 s

So, putting these values in the above formula, we get:

Speed = \(\frac{50 \mathrm{~m}}{20 \mathrm{~s}}\)

= 2.5 m/s

Thus, the speed of scooter is 2.5 metres per second.

**Example Problem 2.**

The train A’ travelled a distance of 120 km in 3 hours whereas another train ‘B’ travelled a distance of 180 km in 4 hours. Which train travelled faster?

**Solution:**

In order to solve this problem, we have to calculate the speeds of both the trains separately. The train having higher speed will have travelled faster.

(i) We know that: Speed = \(\frac{\text { Distance travelled }}{\text { Time taken }}\)

Now, Distance travelled by train A = 120 km

And, Time taken by train A = 3 h

So, Speed of train A = \(\frac{120 \mathrm{~km}}{3 \mathrm{~h}}\)

= 40 km/h …………….. (1)

Thus, the speed of train A is 40 kilometres per hour.

(ii) Again, Speed = \(\frac{\text { Distance travelled }}{\text { Time taken }}\)

Now, Distance travelled by train B = 180 km

And, Time taken by train B = 4 h

So, Speed of train B = \(\frac{180 \mathrm{~km}}{4 \mathrm{~h}}\)

= 45 km/h …………….. (2)

Thus, the speed of train B is 45 kilometres per hour.

From the above calculations we find that train A travels a distance of 40 kilometres in one hour whereas train B travels a distance of 45 kilometres in one hour. It is obvious that train B travelled faster than train A.

**Example Problem 3.**

Salma takes 15 minutes from her house to reach her school on a bicycle. If the bicycle has a speed of 2 m/s, calculate the distance between her house and the school.

**Solution:**

In this problem, the speed is given in m/s (metres per second) and the time is given in minutes. So, before putting in the formula for speed, we will have to convert time from minutes into seconds (by multiplying the minutes by 60). Let us solve the problem now.

Here, Speed = 2 m/s .

Distance travelled = ? (To be calculated)

And, Time taken = 15 minutes

= 15 × 60 seconds (1 minute = 60 seconds)

= 900 s (s = second)

Now, putting these values of speed and time in the formula :

Speed = \(\frac{\text { Distance travelled }}{\text { Time taken }}\)

We get, 2 = \(\frac{\text { Distance travelled }}{900}\)

So, Distance travelled = 2 × 900 m

= 1800 m

Thus, the distance between Salma’s house and her school is 1800 metres.

**Example Problem 4.**

A car moves with a speed of 40 km/h for 15 minutes and then with a speed of 60 km/h for the next 15 minutes. The total distance covered by the car is:

(a) 100 km

(b) 25 km

(c) 15 km

(d) 10 km

**Solution:**

In the first case the speed of car is 40 km/h and in the second case the speed of car is 60 km/h but the time is the same in both the cases, which is 15 minutes. Now, since the speeds are in kilometres per hour (km/h), we should first convert the time of 15 minutes into hours by dividing it by 60. So, time = \(\frac{15}{60}\) hours which is equal to \(\frac{1}{4}\) hour or 0.25 hour. Another point to be noted is that ‘distance covered’ means ‘distance travelled’. Let us solve the problem now.

(i) In the first case :

Distance travelled = Speed × Time taken

= 40 × 0.25 km

= 10 km ……………. (1)

(ii) In the second case

Distance travelled = Speed × Time taken

= 60 × 0.25 km

= 15 km ………………..(2)

Total distance travelled = 10 km + 15 km

= 25 km

Thus, the total distance travelled (or total distance covered) by the car is : (b) 25 km.

**Example Problem 5.**

The odometer of a car reads 57321.0 km when the clock shows the time 8.30 AM. What is the distance moved by the car if at 8.50 AM, the odometer reading has changed to 57336.0 km ?

(a) Calculate the speed of the car in km/min during this time.

(b) Express the speed in km/h also.

**Solution:**

We will first calculate the distance moved by the car.

Here, Initial reading of odometer = 57321.0 km

And, Final reading of odometer = 57336.0 km

Now, Distance moved by the car = Final reading – Initial reading

= 57336.0 – 57321.0 km

Or, Distance travelled = 15 km ……………… (1)

Thus, the distance moved by the car (or distance travelled) is 15 kilometres.

We will now find the time taken by the car to travel this distance. The time taken will be given by the difference in the two clock readings. So, the time taken by the car is from 8.30 AM to 8.50 AM which is 20 minutes (or 20 min).

Thus, Time taken = 20 min ……………. (2)

(a) We know that : Speed = \(\frac{\text { Distance travelled }}{\text { Time taken }}\)

Speed = \(\frac{15 \mathrm{~km}}{20 \mathrm{~min}}\)

= \(\frac{3}{4}\) km / min

= 0.75 km/min

Thus, the speed of car is 0.75 kilometre per minute.

(b) In order to express the speed in km/h (kilometres per hour) we have to first convert the time of 20 minutes into hours (by dividing it by 60). Now,

Distance travelled = 15 km

And, Time taken = 20 minutes

= \(\frac{20}{60}\) hours

= \(\frac{1}{3}\) h (h = hour)

Now, Speed = \(\frac{\text { Distance travelled }}{\text { Time taken }}\)

= \(\frac{15 \mathrm{~km}}{\frac{1}{3} \mathrm{~h}}\)

= \(\frac{15 \times 3}{1}\) km/h

= 45 km/h

Thus, the speed of car is 45 kilometres per hour.