Average speed is an interesting concept in mathematics and physics. The average speed is certainly different from the top or maximum speed. Suppose a sports car reaches a speed maximum speed of 250 km/h. However, its average speed during the trip comes out to be only 50 km/h. Although this seems like a low figure for a sports car, this is how average speed works. Learn the average speed formula.

**What is Average Speed?**

The average speed of an object refers to the total distance it travels divided by the time which is elapsed. Furthermore, this time is elapsed, so as to cover that particular distance. Moreover, the average speed is certainly a scalar quantity because it is defined by a magnitude only.

The average speed of an object is an indication of the average rate at which it covers a particular distance. So, if a car’s average speed is around 60 km/h, this means that the car’s position would change by 60 km/h on the average. Average speed is certainly a rate.

In kinematics, the rate happens to be the quantity divided by the time taken to get that quantity. One can view the average speed as the rate of change in the distance which takes place in relation to time.

**Average Speed Formula**

The expression of the formula for average speed takes place as follows:

_{savg} = ΔD/Δt

D = distance, meters (m)

t = time,sec (s)

Δ = short form for ‘the change’

ΔD = short form for ‘the change in distance’

ΔD = D_{1} + D_{2} + D_{3} + …D_{n}

Δt = short form for ‘the change in time’

Δt = t_{1} + t_{2} + t_{3} + … t_{n}

**Average Speed Formula Derivation**

Imagine a straight line which has two points A and B. Then, an individual move from point A to point B with a particular speed of x. However, on returning from point B to point A, the individual moves at a speed of y. Furthermore, one must consider the distance between points A and B as D.

Therefore, the total distance which the individual travels is: D + D = 2D.

Time taken by the individual to travel point A to B = D/x

Time taken by the individual from point B to A = D/y

Therefore, the total time which the individual takes during his entire journey = D/x + D/y

Then, the avg speed = The total distance/ total time

Hence, average speed = \(\frac{2D}{\frac{D}{x} + \frac{D}{y}}\) = \(\frac{2xy}{x + y}\)

**Solved Example on Average Speed Formula**

Q1. A vehicle travels 600 m in 3 minutes of time. Find out the average speed of the vehicle?

Answer: The distance which the vehicle travels is 600 m. Furthermore, the time it takes to cover the particular distance t = 3 minutes, 3 × 60 = 180 seconds. Now one can certainly apply the formula.

s = D/t

s = 600 / 180

s = 3.333 m/s

Hence, avg speed = 3.333 m/s.

Q2. An individual drives from point A to point B. An individual drives 50 meters in the first hour. Then the individual drives 40 meters in the second hour. Finally, the individual drives 30 meters in the third hour of driving?

Answer: The total distance traveled ΔD = 50 + 40 + 30 = 120 meters

Now, the time Δt = 1 + 1 +1 = 3 hours. This turns out to be 3 × 60 × 60 = 10800 seconds.

Then, one can apply the formula:

s = ΔD/ Δt

s = 120 / 10800

s = 0.011 m/s.

Hence, the avg speed is 0.011 m/s.

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