Final answer:
To determine the total distance traveled by the rock after 4 seconds, integration should be used since it allows for calculating the area under a velocity-time graph, which corresponds to the total distance.
Step-by-step explanation:
To determine the total distance traveled by the rock after 4 seconds, you would use integration. This is because when you have the velocity of an object as a function of time, the total distance travelled can be found by calculating the area under the velocity-time graph, which is achieved through integration.
Differentiation or derivation is used to find the rate of change of a quantity, while antiderivation is another term for integration, though it is less commonly used in this context.
Acceleration is related to this topic as it's the rate of change of velocity. If the acceleration is constant, for example, the velocity-time graph would be a straight line, and the area under that line (the distance) would be a simple geometric calculation.
However, if acceleration varies, you'll need to integrate the velocity function over the specified time interval to find the distance.
The method that should be used to determine the total distance traveled by the rock after 4 s is integration.
Integration is a mathematical operation that calculates the area under a curve. In this case, the curve represents the velocity of the rock over time. By integrating the velocity function over the interval from 0 to 4 seconds, you can find the total distance traveled by the rock.