I'm unsure of why the position of the car will be given by the integral of v(t), my guess is that by using the limits and finding the are under the curve in the graph it will give the distance thus giving the position.
Question:
Assume that a car moves along a straight road with a velocity v(t), where v(t) is a known function of the time t. Explain why the position x(t) of the car after a time t=T will be given by the integral of v(t) between t=0 and t=T.
(assuming that x(0)=0 at time t=0)?
Here is my answer of how I think it works, I'm not too sure though and would like a longer answer showing better understanding but I can't really visualise it since there is x, v, and t, so I can't figure out a graph for it.
Answer: This will be given since by integrating with the limits t=T and t=0 it will work out the area under the curve.
Is my answer correct?