# Initial Velocity Formula

The velocity at which motion start is termed as Initial Velocity. It is the velocity at time interval t = 0 and it is represented by u.

They are four initial velocity formulas.

(1) If final time, acceleration and velocity are provided. The initial velocity is articulated as,

u =v – at

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

u= v– 2as

(3) If distance, acceleration and time are provided. The initial velocity is

$u = \frac{s}{t}-\frac{1}{2}at$

Where,
Initial velocity = u,
Final Velocity = v,
time taken = t,
distance travelled or displacement = s,
acceleration = a

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

$u = 2\left ( \frac{s}{t} \right )-v$

Initial Velocity formula is made use of to find the initial velocity of the body if some of the quantities are given. Initial velocity is articulated in meter per second (m/s).

Initial Velocity Solved Examples

Below are some problems based on Initial velocity which may be helpful for you.

Problem 1: Johny completes the bicycle ride with the final velocity of 10 ms-1 and acceleration 2 ms-2 within 3s. Calculate the initial velocity.

Answer:

Given:

v (Final velocity) = 10 ms-1
a (Acceleration) = 2ms-2
t (Time taken) = 3 s
u (Initial velocity) = ?

v (Final velocity) = u + at

u (Initial velocity) = v – at

u = 10  – (2×3)

u = 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?

Answer:

Given:

Distance s = 100m
(Final velocity) v = 40 ms-1
(Acceleration) a = 6ms-2

(Initial velocity) u2 = v2 – 2as

u2= 1600 – (2 × 6 × 100)

u2= 1600 – 1200

u2= 400 ms-1

∴ (Initial velocity) u = 20 ms-1.