Question

A person moves with a constant speed of 2 m/s due
north and covers a distance of 8 m and then covers a
distance of 6 m due east with a constant speed of 3
m/s. His magnitude of average velocity for his entire
journey is​

Answer 1

$\star$ Given :

• A person moves with a constant speed of 2 m/s due  north and covers a distance of 8 m and then covers a  distance of 6 m due east with a constant speed of 3  m/s

$\star$ To Find :

• Magnitude of average velocity for his entire  journey

$\star$ Concept :

$\star$ Average Velocity :

• Average velocity is defined as Total displacement per total time

$\star$ Solution :

Here , A person moves with a constant speed of 2 m/s due  north and covers a distance of 8 m and then covers a  distance of 6 m due east with a constant speed of 3  m/s

So ,

1 . Via North

Speed = 2 m/s

Distance = 8 m

We know that ,

Speed = Distance / Time

⇒ Time = Distance / Velocity

⇒ Time = 8 / 2

⇒ Time = 4 s

2 . Via East

Distance = 6 m

Speed = 3 m/s

⇒ Time = Distance / Speed

⇒ Time = 6 / 3

⇒ Time = 2 s

Now , Displacement is the shortest distance & difference between final & initial points .

Let the displacement be x

[ Find attachment ]

Apply Pythagoras theorem ,

⇒ 8² + 6² = x²

⇒ 64 + 36 = x²

⇒ x = 10

So , Total Displacement = 10 m

Total Time = 4 + 2 = 6 s

$\implies \bf Average\ Velocity=\dfrac{Total\ Displacement}{Total\ Time}\\\ \implies \bf Average\ Velocity=\dfrac{10}{6}\\\\\implies \bf Average\ Velocity=1.67\ m/s$