### Speed (Speed, Distance and Time)

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Ria reached her home late after school because she was cycling at a slow speed whereas her friend Dia reached her home early because she was cycling with greater speed compared to Ria.

In both these examples, the word ‘speed’ has been used. Now, what does the term ‘speed’ mean in mathematics?

__Speed__means how fast something is moving or able to move.In mathematics, speed is measured as the distance covered/travelled per unit time.

**Units of Measurement of Speed**Distance is covered in kilometers and time is in hours, then the unit of measurement of speed is ‘km’ per ‘hour’ or km/hr. If the distance is in meters and time is in minutes, then speed is ‘m’ per ‘min’ or m/min.

__Example:__The speed of the car is 150 kilometers per hour (150 km/h).**Average Speed**

**Illustration 1:**A truck covers a distance of 224 km between Agra and Jaipur in 4 hours. Find its average speed.**Solution:**Average Speed = Total distance covered / Total time taken= 224 km/4 hours

= 56 km/hr.

**Illustration 2:**Find the speed and average speed of a train, which leaves New Delhi at 6 p.m. and reaches Agra next day at 7 a.m. The distance between the two places is 220 km and the total time for stoppage is 1 hour between these two places.**Solution:**Total time taken = 7 p.m. to 7 a.m.= 12 hours

Time for stoppage = 1 hour

Actual time taken = 12 hours – 1 hour = 11 hour

Speed = Total distance covered / Total time taken

= 220 km/11 hours

= 20 km/hr.

**Illustration 3:**The speed of train is 108 km/h. Find its speed in meters per second.**Solution:**1km = 1000mTherefore 108 km = 108 x 1000 =

**108,000 m**1 min = 60 sec

Therefore, 1 hr. = 60 x 60 =

**3600 sec**Speed = Distance / Time = 108,000/3600 = 30 m/sec

**Illustration 4:**A bus travels at a speed 50 m/s. Find its speed in km/h.**Solution:**Distance travelled by bus in 1 sec = 50 mDistance travelled by bus in 1 hr = 50 x 3600 m (1hr = 3600 sec)

1m = 1/1000km

Speed = 50 x 3600 / 1000 = 180 km/hr.

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