Rectilinear Motion - Average Velocity

• Average velocity tells how fast an object changes its position in a certain direction during a time interval.
• It depends on both the starting and ending positions of the object.
• Since displacement considers direction, average velocity also shows direction.
• Average velocity is different from average speed because it is a vector (it considers direction).
• It is important for understanding motion in physics.

"Average velocity is defined as the displacement of the object during the time interval over which average velocity is being calculated, divided by that time interval."

To calculate average velocity:

• Take the initial position vector of the object (\[\vec x_1\]) at the starting time (t₁).
• Take the final position vector (\[\vec x_2\]) at the ending time (t₂).
• Find the displacement: \[\vec x_2\] − \[\vec x_1\].
• Calculate the time interval: t₂ − t₁.
• Divide the displacement by the time interval to get the average velocity.
• The direction of the average velocity is the same as the direction of the displacement.

• Tells how quickly and in which direction an object changes its position.
• Helps to describe motion in a straight line.
• Used in physics to solve problems about objects moving from one place to another.
• Essential for calculating other motion-related quantities.

\[\vec{v}_{\mathrm{av}}=\frac{\vec{x}_2-\vec{x}_1}{t_2-t_1}\]

• v_av : average velocity.
• x₂ : final position vector.
• x₁ : initial position vector.
• t₂ : final time
• t₁ : initial time

Dimensions: [L¹M⁰T⁻¹]

• Initial position: x = +2 m at t = 0 minutes
• Final position: x = +4 m at t = 1 minute
• Displacement: 4 m − 2 m = 2 m
• Time interval: 1 − 0 = 1 minute
• Average velocity: \[\frac {2}{1}\] = 2 m per minute
• Direction: Along the +ve x-axis (\[\vec v_{av}\] = 2\[\hat i\] m/min, where \[\hat i\] is a unit vector along x - axis)

• A car traveling east from 10 km to 30 km in 30 minutes: The average velocity is \[\frac {{30} - {10}}{30}\] = 0.67 km/min east.
• A person walking north from home to a shop 100 meters away in 5 minutes: The average velocity is \[\frac {100}{5}\] = 20 m/min north.
• A train moving west from station A to station B, covering 50 km in 1 hour: The average velocity is \[\frac {50}{1}\] $=50$ km/h west.