Motion in 1-D Fundamentals - Velocity

Description:

Rate of change of displacement w.r.t. to time is called Velocity.

• Average Velocity = Total displacement/Total time taken = Δx→/Δt
• Instantaneous Velocity = limΔ t→0 Δx→/Δt = dx→/dt

Magnitude of Instantaneous Velocity is equal to Instantaneous Speed.

• For very small displacement, |displacement→| = distance
• Hence, |displacement→|/time = distance/time

Velocity is a vector quantity. (Velocity can be either positive or negative.

Example Problem

A cyclist moves 20 m towards East from origin O. He then reverses his direction and moves 10 m. Total time taken for the entire motion is 20 s. Comment on the Average Speed and Average Velocity of the cyclist.

Solution

Total Displacement = 20 - 10 = +10 m

Total Distance = 20 + 10 = 30 m

Total time = 20 s

Therefore,

Average Speed = Total Distance/Total time = 30/20 = 1.5 m/s

Average Velocity = Total Displacement/Total time = 10/20 = +0.5 m/s