Initial Velocity Formula

What is Initial Velocity?

The initial velocity of an object at the start of a time interval is represented by v0​ or u. It is one of the most important concepts in kinematics, this branch of physics that studies motion in objects. The understanding of initial velocity helps a student perceive how objects move under the diverse influences of forces like gravity, friction, or applied forces. 

Formula 

They are four initial velocity formulas:

(1) If time, acceleration and final velocity are given, the initial velocity is expressed as

ν = v – at

(2) If final velocity, acceleration, and distance are given we make use of:

ν2 = v2 – 2as

(3) If distance, acceleration and time are given the initial velocity is

Where,

u= Initial velocity,

v= Final Velocity,

t= time taken,

s= distance travelled or displacement,

a= Acceleration 

(4) If final velocity, distance and time are given then initial velocity is, 

Solved Problems 

Problem 1: Johny finishes the bicycle ride with the final velocity of 10 ms-1 and acceleration of 2 ms-2 in 3s. Determine the initial velocity.

Solution:

v (Final velocity ) = 10 ms-1

a (Acceleration ) = 2ms-2 

t (Time taken ) = 3s

u (Initial velocity) =?

v (Final velocity) = u + at

υ (Initial velocity) = v – at

υ = 10  – (2×3)

υ = 4 ms-1

∴ (Initial velocity) u = 4ms-1

Problem 2: A man covers a distance of 100 m. If he has a final velocity of 40 ms-1 and has acceleration of 6 ms-2. Compute his initial velocity.

Solution:

Given,

Distance s = 100m

(Final velocity) v = 40 ms-1

(Acceleration) a = 6 ms-2

υ2=1600 – (2 x 6 x 100)

υ2=1600 – 1200

υ2=400 ms-1

∴ (Initial velocity) u = 20 ms-1.