Formula for calculating initial, instantaneous, and average velocity.

The formula for calculating velocity is one of the important concepts in the learning process as well as in everyday life, both in school and at work. To study and work related to velocity more effectively, let's review how to calculate initial, instantaneous, and average velocity.

Formula for calculating speed.

1. Formula for Velocity Calculation

Velocity is the quantity describing fast or slow motion, determined based on the distance traveled in a unit of time. The greater the velocity, the faster the motion and vice versa.

The formula for velocity is:

V = s/t

Where:
- V: Velocity.
- s: Distance traveled.
- t: Time taken to travel distance s.
- Unit of velocity measurement: m/s or km/h.

Example: A person travels from city A to city B in 2 hours, knowing that these two cities are 100km apart. Calculate the person's travel velocity.

Solution:

Applying the formula, we have: V = s/t = 100/2 = 50km/h.

2. Alternative Velocity Calculation Formula

a. Average Velocity

Average velocity is the velocity that changes over time. In a certain time interval, average velocity is the ratio of change in position over that time interval. Therefore, the average velocity in different time intervals will have different values. Knowing the average velocity allows us to adjust time and work intensity to ensure efficiency and productivity.

The formula for calculating average velocity is

Where:
- Vtb: Average velocity.
- s: Distance traveled.
- t: time needed to travel distance s. Time taken to travel distances s1, s2, ..., sn.

- v1, v2, ..., vn: speeds for distances s1, s2, ..., sn.

Example: A car travels from A to B. The first half of the distance is traveled at a speed of v1 = 39km/h, and the second half is traveled at speed v2. Calculate v2 knowing that the average speed of the car from A to B is 47km/h.

Solution

Let the distance from A to B be S, v be the average speed of traveling from A to B.
The time to travel from A to B is t = s/v = s/47 (1)
t = s/2v1 + s/2v2 = s/(2.39) + s/2v2 (2)
From (1) and (2), it follows that s/47 = s/(2.39) + s/2v2
<=> v2 = 59km/h.

b. Instantaneous Velocity

During the distance traveled, velocity is not constant but changes, called instantaneous velocity. This velocity describes the speed at a specific moment in time.

The formula for calculating instantaneous velocity depends on the moment at which we consider it:

Where:

Position vector as a function of time.
t: Time.

Note: You need to pay attention to the units given in the problem to convert correctly before starting to solve. The velocity unit can be km/h or m/s.

This velocity tells us the specific object velocity at a particular time, while average velocity provides the most general view of speed over a specific time interval. Therefore, depending on each situation and requirements in the exercise, you apply either the formula for instantaneous velocity or average velocity.