Contents

The laws of Physics Topics are used to explain everything from the smallest subatomic particles to the largest galaxies.

## Measuring Speed Formula in Physics Concept & Examples

We need two things to find the speed of a moving object: distance covered (or travelled) by the object and the time taken to cover that distance. So, we can determine the speed of an object if we can measure the distance covered by the moving object and the time taken by it to cover that distance. In Class VI we have learnt how to measure distance with scale, measuring tape, etc. We will learn the measurement of time with clocks and watches later on in this chapter.

**Activity 1**

We will now measure the speed of a ball moving along the ground by performing a simple activity as follows :

(i) Draw a straight line on the ground with chalk powder (or lime) (see Figure). Ask your friend to stand about 1 metre away from this line with a ball in his hand. Keep a watch (or stop watch) ready in your hand.

(ii) Ask your friend to roll the ball gently along the ground in a direction perpendicular to the chalk line. Note the time at the moment the ball crosses the chalk line (see Figure).

(iii) The ball will move a certain distance on the ground and then come to rest (or stop). Note the time again when the ball just stops.

(iv) Measure the distance from the chalk line (where the ball crosses the line) to the point where the ball stops, by using a measuring tape or a scale. This will give us the distance covered by the ball. The difference in the two time readings will give the time taken by the moving ball to cover this distance.

(v) Divide the ‘distance covered’ by the ball by the ‘time taken’ to cover this distance. This will give us the speed of the ball.

Suppose the distance covered by the ball on the ground is measured to be 4 metres and 50 centimetres, and the time taken by the ball to move this distance is measured to be 9 seconds. We can calculate the speed of ball from these readings as follows :

Here, Distance covered by ball = 4 m 50 cm

= 4.50 m

And, Time taken by ball = 9 s

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

= \(\frac{4.50 \mathrm{~m}}{9 \mathrm{~s}}\)

= 0.5 m/s

Thus, the speed of this ball is found to be 0.5 metre per second.

### Speeds of Some Animals

Some animals move slowly and have low speeds whereas other animals can run (or fly) very fast and they can have high speeds. The maximum speeds which can be attained by some of the animals (including human beings) are given below. All the speeds are being given here in the same units of kilometres per hour (km/h) for the sake of comparison.

Maximum Speeds Which Some Animals Can Attain

Name of the animal | Maximum speed | |

1. | Snail | 0.0018 km/h |

2. | Tortoise | 0.216 km/h |

3. | Human walking | 8 km/h |

4. | Mouse (Rat) | 11 km/h |

5. | Squirrel | 19 km/h |

6. | Bluefish | 40 to 46 km/h |

7. | Human sprinter (Fast runner) | 40 km/h |

8. | Rabbit | 56 km/h |

9. | Cheetah | 112 km/h |

10. | Falcon (A fast-flying bird) | 320 km/h |

A superfast train has a speed of 100 to 150 km/h ; a racing car has a speed of about 225 km/h ; a jet aeroplane flies at a speed of around 1000 km/h ; and a military jet has a speed of more than 1500 km/h. The space rocket (which launches satellites into earth’s orbit) attains an enormous speed of about 11 km/s (which is almost 40000 km/h).

The speeds of objects help us to decide which one is moving faster than the other. An object having a higher speed moves faster than another object having a lower speed. For example, an aeroplane having a speed of 800 km/h moves much faster than a train having a speed of 60 km/h.

Please note that in order to compare the speeds of a number of moving objects, the speeds of all the objects should be expressed in the same units. We will now learn how to convert speed from one unit to another by solving some problems.

**Example Problem 1.**

Falcon is a bird which flies with a maximum speed of 320 km/h. Calculate its speed in m/s.

**Solution:**

In this problem, we have been given the speed of falcon in the units of kilometres/hour (km/h) and we have to convert it into the units of metres/second (m/s). In order to do this, we have to remember that 1 kilometre is equal to 1000 metres so that 320 kilometres will become 320 × 1000 metres.

Also, 1 hour is equal to 60 × 60 seconds (This is because 1 hour has 60 minutes and each minute has 60 seconds). So, to convert the speed of 320 kilometres/hour into metres/second, we have to multiply this speed by 1000 and divide it by 60 × 60.

Now, Speed = 320 kilometres/hour

= \(\frac{320 \times 1000}{60 \times 60}\) metres/second

= \(\frac{3200}{36}\) metres/second

= 88.8 m/s

Thus, a speed of 320 km/h is equal to 88.8 m/s.

**Example Problem 2.**

A sprinter (fast runner) attains a maximum speed of 10 m/s. What will be his speed in km/h ?

**Solution:**

Here the speed has been given to us in the units of metres/second and we have to convert it into the units of kilometres/hour. In order to do this, we have to convert 10 metres into kilometres by dividing it by 1000. And since there are 60 × 60 seconds in 1 hour, we have also to multiply 10 by 60 × 60.

Thus, we can convert the speed of 10 metres/second into kilometres/hour by dividing this speed of 10 by 1000 and multiplying it by 60 × 60.

Now, Speed = 10 metres/second

= \(\frac{10 \times 60 \times 60}{1000}\) kilometres/hour

= 36 km/h

Thus, a speed of 10 m/s is equal to 36 km/h.

### Uniform and Non-Uniform Motion

When the speed of an object moving along a straight line path remains the same (or unchanged), we say that the speed is constant. On the other hand, if the speed of an object moving along a. straight line path keeps changing (increasing or decreasing), we say that the speed is not constant. So, depending on the nature of its speed, a moving object may have uniform motion or non-uniform motion.

An object moving along a straight line path is said to have uniform motion if its speed remains constant. An object having uniform motion travels equal distances’ in ‘equal intervals of time’. The motion of a car running at a constant speed is an example of uniform motion. A car running at constant speed will cover equal distances in equal intervals of time.

For example, if a car is running at a constant speed of 10 metres per second, it will cover equal distances of ’10 metres’ in every 1 second’ time interval. In the case of uniform motion, the average speed of the moving object is the same as its actual speed. In everyday life, we seldom (rarely) find objects moving with a constant speed (or uniform motion) over long distances or for long durations of time.

An object moving along a straight line path is said to have non-uniform motion if its speed keeps changing (it does not remain constant). An object having non-uniform motion travels ‘unequal distances’ in ‘equal intervals of time’. The motion of a train starting from a Railway Station is an example of non-uniform motion.

This is because when a stationary train starts from a Railway Station, its speed goes on increasing and it covers more and more distance in each ‘1 second’ time interval. And when the train approaches next station, its speed goes on decreasing due to which it covers less and less distance in each 1 second’ time interval.

Please note that the non-uniform motion (in which the speed of an object keeps changing) is also called accelerated motion. We will now represent the motion of objects by drawing graphs.