An antiderivative of a distance versus time graph is a function that represents the original function's rate of change. It is the inverse process of finding a derivative, and it allows us to determine the distance traveled at a given time.
To find the antiderivative of a distance versus time graph, you can use the reverse power rule, which involves increasing the exponent of each term by one and dividing by the new exponent. You can also use integration by substitution or integration by parts.
Finding the antiderivative of a distance versus time graph allows us to determine the displacement or distance traveled by an object at a specific time. It also helps us understand the behavior of the object and make predictions about its future movement.
Yes, the antiderivative of a distance versus time graph can be negative. This means that the object is moving in the negative direction, and its displacement is decreasing over time. It is important to consider the direction of motion when interpreting the antiderivative.
The antiderivative of a distance versus time graph represents the velocity of an object. This is because velocity is the rate of change of displacement over time, and the antiderivative is the inverse process of finding this rate of change. Therefore, the antiderivative tells us the object's velocity at any given time on the graph.