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Average Speed Formula
Average speed is the average speed of an object over a period of time. A formula for average speed is needed because the speed of moving bodies is not constant but changes over time. Students can use the total time and total distance travelled values even though the speeds are different, and use the Average Speed Formula to find a single value that represents the entire trip. Average speed is important for understanding the speed at which movement is occurring. The speed may change from time to time while driving. In this case, it becomes important to find the average speed in order to get an estimate of how fast the trip will be completed. Here are some special cases and shortcuts that can find the average speed in less than a minute. Students can start by calculating the Average Speed Formula and use this formula to solve some examples from the website of Extramarks.
What Is The Average Speed Formula?
Average speed is an important factor in determining how long a trip will take. Average speed is basically a mechanism that helps calculate the ratio of travel time to distance. It is evident that the speed of the vehicle is constantly changing while driving, which makes finding the average speed even more important. There are several ways to find the average speed of an object or vehicle. Here are the most commonly used average speed finders. This is one of the most used and easiest of all average speed finders. It is best if the speed at which the object moves is the same throughout the journey, i.e. neither increasing nor decreasing. A way to find the average speed is to use division. Dividing the distance travelled by the vehicle by the time travelled by the vehicle gives the answer. The above formula is S = D/T if students interpret S as “speed”, “D” as “distance” and “T” as “time”. Total distance/total time will be the average speed. What is the average speed? The average speed of an object can be defined as the total distance travelled over a specific time interval. It can be calculated by dividing the total distance travelled by the total time taken. If an object travels different distances at different velocities, the average speed of an object is the single speed value that, given the uniform motion of the object, travels the same distance in the same time interval. The average speed of an object is equal to the total distance travelled divided by the total time taken. The formula for average speed is
Average Speed Formula:
This is the simplest case. But what if students have an object that moves at one speed for part of its travel and another at another speed for the rest? In minutes, if the distance from the station to the station is 6 km, what is the speed of the train?
Answer: Expressions cannot be used directly here. As students may have noticed, the train has a different speed from A to B than from B to C. In this case, if the object has different velocities in different sections of the journey, students define the average speed as
Average speed = (total distance travelled during the trip)/(total time spent travelling)
Moving a distance “a” at time t1, a distance “b” at time t2, a distance “c” at time t3, and so on, the average speed of an object is given by the relationship:
Average speed = (a + b + c + …)/ (t1 + t2 + t3 + …). Now students must look at some examples.
Average Speed Formula = total distance which is travelled ÷ total time which is taken
Average Speed Formula Special Cases
Example 1: A truck travels from Haryana to Bangalore at an average speed of 60 km/h. It takes 30 hours. The same road from Bangalore back to Haryana with an average speed of 40 km/h. What is the average speed of the truck on the outbound and inbound trips?
 A) 50 km/h B) 55 km/h C) 48 km/h D) 52 km/h
Answer: students may be tempted to add the velocities and divide by 2 to calculate the average speed. This is incorrect because the average speed is the total distance divided by the total time. First, let’s look at the distance from Haryana to Bangalore. This can be done like this:
Distance = (speed) x (time). So distance = 60 × 30 = 1800 kilometres. Now students need to find the travel time from Bangalore to Haryana. Students can write:
Average speed = (total distance)/(total time) = (1800 + 1800)/(30 + 45) = 3600/75 = 48 km/h. So the correct option here is C) 48 km/h.
So to find the average speed, never use the average formula, just find the total distance travelled and the total time taken. Let’s take a look at some more examples of where a journey completes in its three stages.
Examples On Average Speed Formula
Students should look at some examples to better understand the Average Speed Formula.
Example 1: Using the Average Speed Formula, find the average speed of Sam travelling the first 120 miles in 4 hours and the second 100 miles in another 4 hours.
Solution:
To find the average speed, students need the total distance and the total time. Sam’s total mileage = 200 km + 160 km = 360 km
Total time for Sam = 4 hours + 4 hours = 8 hours
Average speed = total distance that is travelled ÷ total time taken
Average speed = 360 ÷ 8 = 45 km/h
Answer: Sam’s average speed is 45 km/h.
Example 2: A train travels at 80 mph for the first 4 hours and 110 mph for the next 3 hours, then finds the average speed of the train using the Average Speed Formula.
Solution:
The train is believed to be travelling at a speed of 80 miles per hour for the first four hours. Here
S.1
= 80 and
T.1
= 4. The train then travels at a speed of 110 miles per hour for the next 3 hours. As a result,
S.2
= 110 and
T.2
= 3
Average Speed Formula = (80 × 4 + 110 × 3) ÷ (4 + 3)
= (650) ÷ (7) = 92.86 miles per hour
Answer: The average train speed is 92.86 miles per hour.
Example 3: The car is 45 km/h, and he drives for 5 hours, then decides to slow down to 40 km/h for the next 2 hours then calculates the average speed using the Average Speed Formula.
Solution:
Distance I = 45 × 5 = 225 miles
distance II = 40 × 2 = 80 miles
Total Distance = Distance 1 + Distance 2
D = 225 + 80 = 305 miles
Using the Average Speed Formula, total distance travelled ÷ total travel time
Average speed = 305 ÷ 7 = 43.57 m/s.
Answer: The average speed of a car is 43.57 m/s.
Solved examples and practice problems and solutions on the Average Speed Formula can be accessed from the Extramarks website or mobile application.
FAQs (Frequently Asked Questions)
1. How to calculate distance using the Average Speed Formula?
The general formula for average speed is [average speed = distance travelled ÷ total time].
To calculate distance, the Average Speed Formula can be constructed as follows: [distance = average speed * time].
2. How do students calculate time using the Average Speed Formula?
The general Average Speed Formula will be given by [Average speed = Distance ÷ Time].
To calculate time, the Average Speed Formula is formed as follows: [time = distance travelled ÷ average speed].
3. How to use the formula for average speed?
To understand how to use the Average Speed Formula, consider an example. Example: A runner completes his 100 m lap in 40 seconds. After completing the first lap, return to the starting point. Calculate the runner’s average speed. Solution: total distance travelled by the runner = 100 meters
Total time = 40 seconds
So students apply the general formula for average speed
students have,
Average speed = distance ÷ time
The runner’s average speed will be 2.5 m/s.
4. What is the general Average Speed Formula for an object?
The general Average Speed Formula for an object is [average speed = total distance travelled ÷ total time taken]. The SI unit for average speed will always be m/s.