Speed and Velocity

1. Speed: Speed is the distance travelled by an object in a given amount of time without considering the direction.

Formula: Speed = `"Distance traversed" / "Total time."`​

Example 1: If a car covers 40 km in one hour, its speed is 40 km/hour.

• Unit: The unit of speed is meters/second (m/s) in the SI system.
• Type: Speed is a scalar quantity. It only tells how fast something is moving but not in which direction.

2. Velocity: Velocity is the displacement of an object in a specific direction divided by the time taken.

Formula: Velocity = `"Displacement" / "Total time"`​

Example 2: If Ranjit’s displacement from home to school is 1000 meters and he takes 25 minutes, his velocity will be:

Velocity = `"1000 meters" / " 25 minutes"` = `"40 meters" / "60 seconds "`​ = 0.66 m/s

• Unit: The unit of velocity is also meters/second (m/s) in the SI system.
• Type: Velocity is a vector quantity. It tells both how fast something is moving and the direction of movement.

The actual distance traversed by Ranjit from home to school
= AB + BC + CD
= 500 m + 700 m + 300 m = 1500 m.
Total time from home to school = 8 minutes + 11 minutes + 6 minutes = 25 minutes.
Ranjit’s displacement from home to school, AD = 1000 meters. Thus, Ranjit’s velocity when going from home to school.

Velocity= `"Displacement" / "Total time"` = `"1000 metres " / "25 minutes"` = `"40 metres" / "60 seconds "` = 0.66 metres/second

Ranjit’s speed while going to school:

Speed= `"Distance traversed" / "Total time"` = `"1500 metres" / "25 minute"` = `"60 metres" / "60 seconds"` = 1 metre/second

Ranjit did not take the straight route of minimum distance while going to school. Therefore, the magnitudes of his velocity and speed were different. Had Ranjit actually gone by the straight route AD, then the magnitudes of his velocity and speed would have been the same.

Example 3: The straight-line distance between the houses of Sheetal and Sangeeta is 500 m, and that between Sangeeta’s house and school is 1200 m. Also, the straight-line distance between Sheetal’s house and school is 1300 m. Suppose Sheetal takes 5 minutes to reach Sangeeta’s house and then 24 minutes to reach school from there. Then,

Location of the school and houses

Sheetal’s speed along path A = `"Distance"/"Time"` = `"500 m"/"5 minute"` = 100 m/minute

Sheetal’s speed along path B = `"Distance"/"Time"` = `"1200 m"/"24 minute"` = 50 m/minute

Sheetal’s average speed = `"Total distance"/"Total time"` = `"1700 m"/"29 minute"` = 58.6 m/minute

Sheetal’s velocity = `"Displacement"/"Time"` = `"1300 m"/"29 minute"`

Sheetal’s velocity = 44.83 m/minute