# Average Speed Formula

Average speed is the mean value of the speed of a body over a period of time. The formula for average speed is needed since the speed of a moving body is not constant and varies across a period of time. Even with varying speed, the values of total time and the total distance covered can be used, and with the help of the formula for average speed, we can find a single value to represent the entire motion.

## What is the Average Speed Formula?

The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:

### Average Speed Formula:

Average Speed = Total distance covered ÷ Total time taken

### Average Speed Formula Special Cases

**Case 1:** For a body or object traveling with a speed of \(s_1 \) for time \( t_1 \), and the speed of \(s_2 \) for time \( t_2 \), the formula for average speed is given in the below expression. The product of \(s_1 \times t_1 \), and \(s_2 \times t_2 \) gives the distances covered in time intervals \(t_1 \), and \(t_2 \) respectively.

Average Speed Formula \(= \frac{s_1 \times t_1 + s_2 \times t_2}{t_1 + t_2}\)

**Case 2: **Similarly, when 'n' different speeds, \(s_{1}, s_{2}, s_{3},... s_{n}\), are given for 'n' respective individual time intervals, \(t_{1}, t_{2}, t_{3},... t_{n}\) respectively, the average speed formula is given as:

Average Speed Formula \(= \frac{s_1 t_1 + s_2 t_2 + ... + s_n t_n}{t_1 + t_2 +...+ t_n}\)

**Case 3:** Average speed when different distances, \(d_{1}, d_{2}, d_{3},... d_{n}\), are covered for different intervals of time, \(t_{1}, t_{2}, t_{3},... t_{n}\) repectively is given as:

Average Speed Formula \(S_{avg}\) \(= \frac{d_1 + d_2 + d_3 +...+ d_n} {t_1 + t_2 + t_3 +....+ t_n}\)

**Case 4:** Average speed when different speeds, \(s_{1}, s_{2}, s_{3},... s_{n}\), are given for different distances, \(d_{1}, d_{2}, d_{3},... d_{n}\) respectively is given as:

Average Speed Formula \(S_{avg}\) \(= \frac{d_1 + d_2 + d_3 +...+ d_n} {\dfrac{d_1}{s_1} + \dfrac{d_2}{s_2} + \dfrac{d_3}{s_3} +....+ \dfrac{d_n}{s_n}}\)

**Case 5:** Average speed formula when two or more speeds are given (\(s_{1}, s_{2}, s_{3},... s_{n}\)) such that those speeds were traveled for same amount of time (\(t_{1} = t_{2} = t_{3} =... t_{n} = t)\) is given as:

Average Speed Formula, \(S_{avg}\) \(= \frac{s_{1} t + s_{2} t +...+ s_{n} t} {t\times n} = \frac{s_{1} + s_{2} +...+ s_{n}} {n} \)

**Case 6: **Average speed when different speeds given (\(s_{1}, s_{2}, s_{3},... s_{n})\) for same distance (\(d_{1} = d_{2} = d_{3} =... d_{n} = d)\) is given as:

Average Speed Formula \(S_{avg}\) \(= \frac{ n \times d} { d \times \left[ \dfrac{1}{s_1} + \dfrac{1}{s_2} + \dfrac{1}{s_3} +....+ \dfrac{1}{s_n}\right]} = \frac{ n} {\left[ \dfrac{1}{s_1} + \dfrac{1}{s_2} + \dfrac{1}{s_3} +....+ \dfrac{1}{s_n}\right]}\)

## Examples on Average Speed Formula

Let us take a look at a few examples to better understand the formula for average speed.

**Example 1: **Using the average speed formula, find the average speed of Sam, who covers the first 200 kilometers in 4 hours and the next 160 kilometers in another 4 hours.

**Solution: **

To find the average speed we need the total distance and the total time.

Total distance covered by Sam = 200Km + 160 km = 360 km

Total time taken by Sam = 4 hour + 4 hour = 8 hour

Average Speed = Total distance covered ÷ Total time taken

Average Speed = 360 ÷ 8 = 45km/hr

**Answer:** Average speed of Sam is 45 km/hr.

**Example 2: **A train is moving with a speed of 80 miles per hour for the first 4 hours and 110 miles per hour for the next 3 hours. Find the average speed of the train with the help of the average speed formula.

**Solution:**

It is given that the train is moving at a speed of 80 miles per hour for the first 4 hours.

Here \(S_1 \) = 80 and \(T_1 \) = 4.

And the train is moving at a speed of 110 miles per hour for the next 3 hours.

Hence \(S_2 \) = 110 and \(T_2\) = 3.

Average Speed Formula = \(\frac{S_1 \times T_1 + S_2 \times T_2}{T_1 + T_2}\)

Average Speed = (80 × 4 + 110 × 3) ÷ (4 + 3)

= (650) ÷ (7) = 92.86 miles/hour

**Answer:** The average speed of the train is 92.86 miles/hour.

**Example 3: **A car travels at a speed of 45 km/hr for 5 hours and then decides to slow down to 40 km/hr for the next 2 hours. Calculate 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 average speed formula = Total distance traveled ÷ Total time taken

Average Speed = 305 ÷ 7 = 43.57 m/s.

**Answer: **Average speed of a car is 43.57 m/s.

## FAQs on Average Speed Formula

### How to Calculate Distance Using Average Speed Formula?

The general formula for average speed is given as [Average Speed = Distance Traveled ÷ Total Time Taken]

To calculate the distance, the average speed formula can be molded as [Distance = Average Speed × Time].

### How to Calculate Time Using Average Speed Formula?

The general average speed formula is given as [Average Speed = Distance ÷ Time]

To calculate the time, the average speed formula will be molded as [Time = Distance Travelled ÷ Average Speed].

### How to Use the Formula for Average Speed?

To understand how to use the formula for average speed let us consider an example.

Example: A runner completes a 100m lap in 40 sec. After the finish of the first lap, he reached back to the starting point. Calculate the average speed of the runner.

Solution: Total distance covered by the runner = 100 meters

Total time = 40 sec

So, applying the general formula for the average speed

we have,

Average Speed = Distance ÷ Time

Average Speed = 100 ÷ 40 = 2.5m/s.

The average speed of the runner is 2.5m/s.

### What will Be the General Average Speed Formula for an Object?

The general speed average formula for an object is given as [Average Speed = Total Distance Traveled ÷ Total Time Taken]. SI unit of average speed is m/s.

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