Instantaneous speed is the speed of an object at a specific moment in time, or at a specific point along its trajectory. It is the rate at which an object is moving at that exact instant, and it can be different from the average speed over a longer period of time.
Instantaneous speed can be calculated by taking the derivative of an object's position with respect to time. This means finding the slope of the tangent line at a specific point on a position-time graph. It can also be calculated by taking the limit of the average speeds over shorter and shorter time intervals.
Acceleration is the rate at which an object's velocity changes over time. This means that acceleration is directly related to an object's instantaneous speed - the greater the acceleration, the faster the object's speed changes at a specific moment in time.
Yes, instantaneous speed can be negative if the object is moving in the opposite direction of its positive direction. For example, if an object is moving right with a positive velocity and then changes direction to move left, its instantaneous speed will be negative at the point where it changes direction.
Average speed is calculated by dividing the total distance traveled by the total time taken. It gives an overall representation of an object's speed over a period of time. Instantaneous speed, on the other hand, only represents the speed at a specific moment and can change constantly throughout an object's motion.