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Average Speed

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As a runner completes a lap of a running track we can calculate his average speed from the distance round the track and the time taken to run round. During the lap his speed will vary and average speed calculation will gives the average value of his speed. The average speed play an important rule when the speed is not uniform.

In case speed is not uniform, we obtain average speed by dividing the total distance covered by the total time taken. In this section we will learn more about average speed.

What is Average Speed?

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The average speed of an object over a given time interval is the total distance traveled divided by the total time taken.

Average Speed Formula

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The formula for the calculating the average speed of an object move from one source to another destination distance is

$Average\ Speed$ = $\frac{Total\ distance\ travelled}{Total\ time\ taken}$

Average speed is a scalar quantity. The SI unit of speed is meters per second (m/s).

By rearranging the formula gives,

$Total\ distance\ travelled$ = $Average\ Speed \times Total\ time\ taken$

And

$Total\ time\ taken$ = $\frac{Total\ distance\ travelled}{Average\ Speed}$

Average Speed and Average Velocity

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Average speed is defined as the total distance travelled divided by the total time taken. Average speed is a scalar quantity.

$Average\ Speed$ = $\frac{Total\ distance\ travelled}{Total\ time\ taken}$

The velocity of an object is defined as the displacement divided by the time internal during which the displacement occurred. Since displacement is a vector quantity, average velocity is also a vector quantity.

$Average\ Velocity$ = $\frac{Net\ displacement }{Total\ time\ taken}$

Average Speed Examples

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Average speed of Some objectives are given below.

Object Speed in km/h
Average speed of a snail 0.01
Average speed of a tortoise 0.5
Average speed of a man walking at a steady pace 6
Average speed of sprinter P.T Usha in 200 metres dash 30

Average Speed Problems

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The following are the problems of average speed.

Solved Examples

Question 1: If a car travels 600km in 6 hrs, 500km in 7 hrs, and then 200 km in 1.5 hrs, than find the average speed of car?
Solution:
 
By Using the formula of the Average Speed :

$Average\ Speed$ = $\frac{Total\ distance\ travelled}{Total\ time\ taken}$

Total distance travelled = $600 + 500 + 200$

Total time taken = $6 + 7 + 1.5$ 

$Average\ Speed$ = $\frac{600 + 500 + 200}{6 + 7 + 1.5}$

$Average\ Speed$ = $\frac{1300}{14.5}$

$Average\ Speed$ = $89.655$ km/hr.

Hence, the average Speed of car is $89.655$ km/hr

 

Question 2: A train traveled 5 hours at a rate of 75 mph and for 3 hours at 70 mph. What was the average speed of the train?
Solution:
 
$Total\ distance$ = $75 \times 5$ + $70 \times 3$ = $375 + 210$ = $585$

$Total\ time$ = $5 + 3$ = $8$

$Average\ speed$ = $\frac{Total\ distance}{Total\ time}$

$Average\ speed$ = $\frac{585}{8}$ = $73.125$

Average speed of the train was $73.125$ mph.

 

Question 3: If a person can walk with an average speed of 2 meters/second, how far will they walk in 4 minutes?
Solution:
 
There are 60 seconds in 1 minute

$Time\ taken$ = $4 \times 60$ seconds = $240$ seconds

$Average\ speed$ = $2$ m/s

We know that  $Average\ speed$ = $\frac{Total\ distance}{Total\ time}$

then $Total\ distance\ travelled$ = $Average\ Speed \times Total\ time\ taken$

Therefore $Total\ distance\ travelled$ = $2 \times 240$  = $480$ meters.