Velocity is a measure of how fast an object is moving and in what direction. It is a vector quantity, which means that it has both magnitude and direction. Velocity is usually represented by the symbol “v,” and it is measured in meters per second (m/s) or other units of length per time. There are several formulas for velocity, but three of the most commonly used ones are:
- Average velocity formula: Average velocity is the total displacement of an object over a given time interval, divided by the time interval. The displacement is the change in position of the object from its initial position to its final position. The average velocity formula is:
v = Δx/Δt
Where:
- v: average velocity (m/s)
- Δx: displacement (m)
- Δt: time interval (s)
This formula assumes that the object moves at a constant velocity over the time interval, which means that its acceleration is zero. If the object accelerates during the time interval, the average velocity formula will not give the instantaneous velocity at any point during the interval.
- Instantaneous velocity formula: Instantaneous velocity is the velocity of an object at a specific instant in time. It is the limit of the average velocity as the time interval approaches zero. The instantaneous velocity formula is:
v = lim Δt->0 Δx/Δt = dx/dt
Where:
- v: instantaneous velocity (m/s)
- Δx: displacement (m)
- Δt: time interval (s)
- dx/dt: derivative of the position function with respect to time (m/s)
This formula gives the exact velocity of the object at any given moment in time, regardless of whether its velocity is constant or changing. It is derived from calculus, which allows us to find the slope of the tangent line to the position-time graph of the object at a specific point.
- Final velocity formula: Final velocity is the velocity of an object at the end of a motion or after a given time interval. It is related to the initial velocity, the acceleration, and the time interval. The final velocity formula is:
v = u + at
Where:
- v: final velocity (m/s)
- u: initial velocity (m/s)
- a: acceleration.