Average Speed Formula
Average speed is a fundamental concept in physics that describes the overall rate at which an object moves over a given period of time. It is defined as the total distance traveled divided by the total time taken to cover that distance. A formula for average speed is needed because the speed of moving bodies is not constant but changes over time.
Unlike instantaneous speed, which can vary at different moments during a journey, average speed provides a single value that summarizes the overall motion of the object. This measure is crucial in various practical applications, from planning travel itineraries to analyzing the performance of vehicles and athletes.
In this article, we have discussed the average speed, the average speed formula, and use this formula to solve some examples.
What is Average Speed?
Average speed is a measure that quantifies the overall rate of motion of an object over a given period of time. It is calculated by dividing the total distance traveled by the total time taken to travel that distance. Unlike instantaneous speed, which can vary at different moments, average speed provides a single value representing the general pace of movement over a journey. For example, consider a car trip where a driver travels 150 kilometers in 3 hours. The average speed for the trip can be calculated using the formula: 150/3 = 5 hours.
This means that, on average, the car traveled at a speed of 50 kilometers per hour, even though its speed may have varied at different points during the trip due to traffic conditions, stops, or accelerations.
Average Speed Formula
The speed of an object is calculated by dividing the distance it travels by the time it takes to cover that distance. If ‘D’ is the distance travelled in some period ‘T’, then the speed (S) of the object for this trip,
Total Distance traveled/Total Time taken ………… (1)
 "{S_{AVG}}= \frac{D_{total}}{T_{total}}\, ..........(2)")
We will learn about the average speed formula, including how to compute it and how to determine the time or distance given the average speed.
How to Calculate Average Speed?
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. There are several ways to find the average speed of an object or vehicle.
Average Speed = Total distance covered ÷ Total time taken
Average Speed Formula With Three Speeds
The average speed formula for two speeds may be computed by summing the entire distance and dividing it by the total time taken to cover it.
- We must now determine the two distances if two speeds and the time it takes for them are provided.
- The formula for calculating distance covered is distance = speed × time.
- Next, we sum the two distances and divide them by the total time.
For example, 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 Formula = (a + b + c + …)/ (t1 + t2 + t3 + …)
Average Speed Formula Special Cases
The table below summarizes the special Cases of the average speed formula:
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Average Speed Formula Special Cases
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Average Speed Formula |
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For a body or object traveling with a speed of s1 for time t1, and the speed of s2 for time t2 , The formula for average speed is given here. The product of s1×t1, and s2×t2 gives the distances covered in time intervals t1, and t2 respectively.
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$$Savg = \frac{s_1 \times t_1 + s_2 \times t_2}{t_1 + t_2}$$ |
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Similarly, when ‘n’ different speeds, s1, s2, s3….sn are given for ‘n’ respective individual time intervals, t1, t2, t3.…tnrespectively, the average speed formula is given as:
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$$Savg = \frac{s_1 t_1 + s_2 t_2 + … + s_n t_n}{t_1 + t_2 +…+ t_n}$$ |
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Average speed when different distances, d1, d2, d3.…dn, are covered for different intervals of time, t1, t2, t3.…tn respectively is given as:
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$$Savg = \frac{d_1 + d_2 + d_3 +…+ d_n} {\dfrac{d_1}{s_1} + \dfrac{d_2}{s_2} + \dfrac{d_3}{s_3} +….+ \dfrac{d_n}{s_n}}$$ |
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Average speed when different speeds, s1, s2, s3….sn, are given for different distances, d1, d2, d3.…dn respectively is given as:
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$$Savg = \frac{d_1 + d_2 + d_3 +…+ d_n} {\dfrac{d_1}{s_1} + \dfrac{d_2}{s_2} + \dfrac{d_3}{s_3} +….+ \dfrac{d_n}{s_n}}$$ |
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Average speed formula when two or more speeds are given (s1, s2, s3….sn) such that those speeds were traveled for same amount of time (t1= t2 = t3 = ….tn=t) is given as:
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$$Savg= \frac{s_{1} t + s_{2} t +…+ s_{n} t} {t\times n} = \frac{s_{1} + s_{2} +…+ s_{n}} {n}$$ |
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Average speed when different speeds given (s1, s2, s3….sn) for same distance (d1= d2 = d3 = ….dn = d) is given as:
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$$Savg= \frac{ n \times d} { d \times \left[ \dfrac{1}{s_1} + \dfrac{1}{s_2} + \dfrac{1}{s_3} +….+ \dfrac{1}{s_n}\right]} = \frac{ n} {\left[ \dfrac{1}{s_1} + \dfrac{1}{s_2} + \dfrac{1}{s_3} +….+ \dfrac{1}{s_n}\right]}$$ |
Note – 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 : 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
Solution : 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)
Average speed = (1800 + 1800)/(30 + 45)
Average speed = 3600/75
Average speed = 48 km/h.
Answer: The correct option here is C) 48 km/h.
Example 2: 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 3: 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
S1 = 80 and T1 = 4
The train then travels at a speed of 110 miles per hour for the next 3 hours. As a result,
S2 = 110 and T2 = 3
Average Speed Formula = (80 × 4 + 110 × 3) ÷ (4 + 3)
Average Speed Formula = (650) ÷ (7)
Average Speed Formula = 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.