# Initial Velocity Formula

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

They are four initial velocity formulas:

(1) If time, acceleration and final 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 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.

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.

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.