why acceleration at any instant does not velocity at any instant?
To understand why acceleration at any instant does not equal velocity at any instant, let's first clarify what these two terms represent.
Velocity is a vector quantity that describes the rate at which an object changes its position. It includes both the magnitude and the direction of motion. Acceleration, on the other hand, is also a vector quantity that measures the rate at which velocity changes.
The main distinction between velocity and acceleration lies in their representation of the motion of an object over time. Velocity represents the object's instantaneous speed and direction at a particular moment. In contrast, acceleration represents the rate at which the velocity is changing at that moment.
Mathematically, velocity is the first derivative of position, while acceleration is the first derivative of velocity with respect to time. This means that to find the acceleration at any instant, you need to take the derivative of the velocity function with respect to time.
Since velocity represents the change in position over time, it does not capture the change in velocity itself. Acceleration, on the other hand, represents the change in velocity, meaning it captures the rate at which velocity is changing over time. Therefore, acceleration can be zero even when the object is moving with a constant velocity, as long as there is no change in its velocity.
To summarize, acceleration and velocity are related but distinct concepts. Velocity represents an object's speed and direction at a given instant, while acceleration represents the rate at which velocity is changing over time.