Motion is a very important concept and activity in the area of Physics. Many terms and factors are relevant in the motion. Such as distance, displacement, speed, times, velocity, etc. Moving objects are having static or varying velocity. Thus initial velocity and final velocity may be different if the motion is having acceleration. Velocity is the rate of the change in the position of an object relative to time. In this article, we see the concept of initial velocity and initial velocity formula with examples. Let us learn the concept!

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**Initial Velocity Formula**

**Concept of initial velocity:**

Equations of the motion are used to describe the behavior of a physical system in terms of its motion. The relations between various terms and quantities are known as the equations of motion. In the case of uniform acceleration, there are mainly three equations of motion which are also called the laws of constant acceleration.

Forces acting on any object will cause it to accelerate. Due to this acceleration velocity of the object changes. Therefore, the initial velocity is the velocity of the object before the effect of acceleration, which causes the change. After accelerating the object for some amount of time, the velocity will be the final velocity.

**Formulas for Initial Velocity**

Thus velocity at which motion start is the initial velocity. Obviously, this velocity at time interval t = 0. It is represented by letter u. Three initial velocity formulas based on equations of motion are given below,

- If time, acceleration and velocity are known. The initial velocity is formulated as

u =v â€“ at

- If final velocity, acceleration, and distance are known then we can use the formula as:

uÂ² = vÂ² â€“ 2as

- If distance, acceleration and time are known. Then the initial velocity will be computed as:

u = \(\frac {s} {t} â€“ {1}{2} a t\)

Where,

u | Initial velocity |

v | Final Velocity |

t | time taken |

s | displacement |

a | acceleration |

Initial Velocity formulas are used to find the initial velocity of the moving body if some of the terms are given. Initial velocity can be formulated in a unit of a meter per second i.e. \(ms^{-1}.\)

**Solved Examples**

Q.1: A train is moving through a city with a slow speed. Once outside the city, the train accelerates at 0.40 \(ms^{-2}\) for 60.0 s. After this acceleration, the velocity of the train is 30.0 \(ms^{-1}\). Determine the initial velocity of the train.

Solution:

As given terms are,

t = 60.0 s

a = 0.40 \(ms^{-2}\)

v = 30.0 \(ms^{-1}\)

Thus, the initial velocity is:

u =v â€“ at

i.e. u = 30 â€“ (0.40) Ã—(60.0)

u = 30 â€“ 24

u = 6 \(ms^{-1}\)

Therefore, the initial velocity of the train was 6.0 \(ms^{-1}\).

Q.2: A boy covers a distance of 100 m. If his final velocity was 40 \(ms^{-1}\) and has acceleration of 6 \(ms^{-2}\). Compute his initial velocity?

Answer:

Given parameters are:

Distance, s = 100m,

Final velocity, v = 40Â \(ms^{-1}\)

Acceleration, a = 6Â \(ms^{-2}\)

Thus we will use the formula:

uÂ² = vÂ² â€“ 2as

i.e. uÂ² = 40Â² â€“ 2Â Ã— 6Â Ã— 100

= 1600 â€“ 1200

= 400

thus u = 20 \(ms^{-1}\)

Therefore, the initial velocity of the boy was 20 \(ms^{-1}.\)

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