instantaneous velocity
derivative of position s'(t)
Instantaneous velocity refers to the velocity of an object at a specific point in time. It is the rate at which an object changes its position with respect to time at a particular moment. The unit of instantaneous velocity is meters per second (m/s) or any other unit of distance divided by time.
The formula for instantaneous velocity is given as:
instantaneous velocity = lim Δt→0 [(change in displacement) / (change in time)]
This equation states that the instantaneous velocity can be determined by finding the limit of the average velocity as the time interval approaches zero.
For example, if a car is travelling at a constant velocity of 30 m/s, its instantaneous velocity at any given point in time will also be 30 m/s. However, if the car starts to accelerate, its instantaneous velocity will change, and its velocity at any moment will depend on its acceleration.
Therefore, to find the instantaneous velocity of a moving object, we need to know the change in displacement, change in time and the limit of the average velocity. In other words, it is the velocity at a given instant in time, as opposed to the average velocity over a longer period of time.
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