Physics/Question pertaining to a position vs time graph
What is the position of the motorcyclist at t = 40 s? What is the distance traveled by the motorcyclist in the first 40 s?
the easiest way to answer this question is to convert the acceleration-time graph into a velocity-time graph. Once you have the velocity-time graph you can determine the displacement by calculating the areas under the graph! When determining the displacement any area below the x-axis is negative while any area above the x-axis is positive. For purposes of distance all of the areas are treated as being positive since distance, unlike displacement, is a scalar quantity.
Step one: Calculate the velocities at all applicable inflection points by determining the corresponding areas under the acceleration-time graph (A)
Step two: Plot the velocity-time graph.
Step three: Calculate the areas under the graph (B)
Step four: Add up the areas to determine the Displacement and Distance (C)
See attached image for the details!