## Introduction

Average speed is a crucial factor to learn the time it takes to complete a journey. Average speed is essentially a mechanism that helps us calculate the rate of travel time and distance. It is evident that the speed keeps on changing in the journey, making finding the average speed more important. There are several ways of finding the average speed of an object or vehicle. The most commonly used average speed finder is mentioned below.

This is the most commonly used and one of the easiest methods of all average speed finders. It is most desirable in cases where the speed with which the object travels is the same throughout the journey, meaning it neither increases nor decreases. The procedure of finding the average Speed is to use division. Divide the distance the vehicle covers by the time the vehicle covers, and you have the answer.

The formula of the above is S = D/T if “S” is considered “speed,” “D” is taken as “distance,” and “T” is interpreted as “time.” In other words, total distance / total time = Average Speed.

### What is Average Speed?

The average speed of an object can be defined as the total distance travelled by it in a particular interval of time. It can be calculated by dividing the total distance travelled by the total time taken.

If an object covers different distances with different velocities, then average velocity of the object is a single velocity value for which if the object moves uniformly, it will cover the same distance in the same interval of time.

Mathematically, average speed (Savg) = \[\frac{\text{Total distance covered}}{\text{Total time taken}}\]

If an object covers x_{1}, x_{2}, x_{3},.......,x_{n} distances in t_{1}, t_{2}, t_{3},.....,t_{n} seconds respectively, then

\[S_{avg} = \frac{x_{1} + x_{2} + . . . . + x_{n}}{t_{1} + t_{2} + . . . . + t_{n}}\]

SI unit of average speed is m/s, and is a scalar quantity, which means it has only magnitude.

### Solved Examples on Average Speed

1. A train travels at a speed of 300 km/hr for 2 hours and then slows down to 220 km/hr for the next 2 hours. What is the average speed of the train?

Solution: Distance covered in the first 2 hours, D1 = 300 * 2 = 600 miles

Distance covered in the next 2 hours, D2 = 220 * 2 = 440 miles

Total distance covered, D= D1 + D2

D = 600 + 440 = 1040 miles

Total time taken = 4 hours

Thus, the average speed of the train = \[\frac{\text{Total Distance travelled (D)}}{\text{Total Time taken (T)}}\]

= 1040/4 = 260 m/s

2. A particle moves with a speed of 4m/s for 20s. It again moves with a speed of 6m/s for another 20s and finally moves with a speed of 8m/s for next 20s. Calculate the average speed of the particle? (in m/s)

Solution: Distance= speed x time

Distance travelled in first 20s, D1 = 20s × 4 m

= 80 m

Distance travelled in next 20s, D2 = 20 × 6 m

= 120 m

Distance travelled in the last 20s, D3 = 20 × 8 m

=100 m

Total distance travelled by particle, D = 80 + 120 + 160 m

= 360 ms

Total time taken, T = 20×3 = 60s

Therefore, the average speed, S = D/T

= 360/60 m/s

= 60 m/s

3. A person goes from Point A to Point B in 10s and returns back in 8s. If the distance between A and B is 36m, find the average speed of the person.

Solution: Here total distance covered = 72m

Total time taken = 18s

Therefore, average speed = \[\frac{\text{Total distance covered}}{\text{Total time taken}} = \frac{72}{18}\] = 4 m/s.

### Practice Questions

A boy cycles at a speed of 12 km/hr for 2 hours and then at 15 km/hr for 1 hour. Find the average speed of the boy.

A car travels at an average speed of 35 mph. How long will the car take to cover a distance of 14.5 miles?

A boy covered a complete cycle along a circular path of radius 35m in 22s. Find the average speed of the boy.

### More Examples on Average Speed

1. Rahul runs 4 miles from his house to the playground in 2 hours every day. What is his average speed?

Ans: Average Speed = total distance ÷ total time

Average Speed = 4 miles ÷ 2 hours

Average Speed = 2 miles per hour

2. Anitya walks from A to B, covering 8 miles of distance, for 2 hours. What is the average speed?

Ans: Average Speed = total distance ÷ total time

Average Speed = 8 miles ÷ 2 hours

Average Speed = 4 miles per hour

Another formula is used when the speed during the journey changes. If an object covers some part of the journey with one speed and changes the speed to cover the other part of the journey, this formula is applied. Let us learn from an example.

3. An aeroplane travels from the United States to Malaysia, a distance of 9000 miles, in 18 hours and travels from Malaysia to India, a distance of 3000 miles in 5 hours.

Ans: To find the average speed of the locomotive, you will have to do the following formula.

Distance travelled = 9000 miles + 3000 miles

Distance travelled = 12000 miles

Time taken = 18 hours + 5 hours

Time taken = 23 hours

Average speed = 12000 / 23

Average speed = 521 mph

## FAQs on Average Speed Formula

**1. What are the examples of Average Speed?**

If a jeep covers a distance of 140 miles in 4 hours, what is the average speed of the jeep?

**The solution is:**

Average speed = Total distance / Total time

Average speed = 140 miles / 4 hours

Average speed = 15 miles / hour

This is an example of the average speed.

**2. How do you find average speed without time and distance?**

To find the average Speed with the only given factor as speed - without time and distance given - add the initial speed to the final speed in the entire journey and divide the answer by 2. What the result comes down to is the average speed.

**For example: ** Speed = initial speed + final speed / 2

Speed = 30 mph + 40 mph / 2

Speed = (30 + 40 ) / 2

Speed = 70 / 2

Speed = 35 mph

This is the formula you can use to find the average Speed without the other given factors such as time and distance. The only given factor is the initial and final speed.

**3. What is the formula for average distance?**

Just as average speed is found out through time and distance being the given factors, the average distance can be calculated through the following formula, with the given factors being average Speed and time.

D = Speed x time

**In other words: **

Distance = average speed x time taken

**A solved example of the average distance finder is as follows:**

Distance = average speed x time

Distance = 130 mph x 1.5 h

Distance = 195 miles

**4. What kind of quantity is the average speed?**

There are two types of quantity: velocity and scalar. The difference between these two is the presence of direction. Since Average Speed deals with distance and speed, it is a scalar quantity. If it had factors of direction and position, it would have been velocity quantity.

**5. How do you find average speed when the distance is equal and the speeds are different?**

A person travelling from Haryana to Mumbai at a rate of 120 miles per hour and back from Mumbai to Haryana at a rate of 130 miles per hour would have the solution to find the average speed like this:

= 2xy / (x+y)

x = Rate at which he travels from Haryana to Mumbai

x = 120

y = Rate at which he travels from Mumbai to Haryana

y = 130

So,

Average Speed = (2 x 120 x 130) / (120 + 130)

Average Speed = 31,200 / 250

Average Speed = 124.8

Therefore, the average speed of the person on this journey is 124.8 miles per hour.