Initial Velocity Formula

Initial Velocity Formula

Initial velocity refers to the velocity in the beginning when the object starts moving. When the time is equal to 0 seconds the velocity is called initial velocity. To denote initial velocity, we use the symbol ‘u’.

Different factors impact initial velocity like distance, speed, displacement, etc. Therefore we calculate the rate of change in the position of a person with respect to time by using different factors. 

The Formula for Calculating Initial Velocity

 To calculate initial velocity, we have four different formulas.

1. When time, final velocity and acceleration are given in the question:

Then time, final velocity and acceleration are given. They are represented by the formula 

u=v+at

Here ‘u’ denotes initial velocity. v denotes final velocity, a denotes acceleration, and t is the time taken. 

2. If velocity distance in acceleration after avoided, then we use this formula

U2= v2 +2as 

Here u is initial Velocity,  V is final velocity a denotes acceleration,, and s equals to the distance. 

3. In case the given variables are distance, acceleration and time that is s, a and t, we use the formula given below to calculate initial velocity: 

u= s/t – ½ at 

4. When we need to calculate initial velocity by using final velocity, distance and time, we can use this formula: 

u= 2/3 (s/t)- v/3

Here s denotes distance or displacement, t refers to time in seconds, v is the final velocity and u is the initial velocity.  

Solved Examples

Example 1: If the final velocity of a person is 10 meters per second, and the acceleration is 2 meters per second, the time taken is 3 seconds. What was the initial velocity of that person?

Ans: v= 10 m/s, a= 2 m/s2, t=3 s 

Using the formula for calculating initial velocity when time, final velocity and acceleration is given, 

u= v+ at

u= 10+2(3) 

u= 10+6 = 16m/s. Hence the initial velocity of that person was 4 m/s. 

Example 2: Suman covers a distance of 100 meters with a velocity of 40 meters per second, and the acceleration throughout this journey was six meters per second square. Find the initial velocity of Suman. 

Solution: Here d= 100 m, v= 40 m/s, a= 6 m/s2, u=? 

Using the formula to compute initial velocity when final velocity, acceleration and distance are given, 

U2= v2 +2as 

U2=  402 + 2(6)(100) 

U2 = 1600+1200 = 2800

Hence U= 52.91 m/s.  

Solved example no. 3: If a car accelerates at 0.40 m/s2 and the time taken by it is 1 minute, and the final velocity that it attains is equal to 30 m/s, find the initial velocity of the car. 

Solution: a = 40 m/s2, t= 60 sec ( 1 minute), v= 30 m/s 

Using the formula when a, t and v are given, 

u= v +at 

U = 30+(0.40)(60)

u= 30+24

u= 54 m/s.