A cyclist begins moving along a straight road at time t=0 seconds. For the next 12 seconds the velocity v(t) of the cyclist (in meters per second) is known to be a continuous, differentiable function.
The total displacement of the cyclist from t=0 to t=12 seconds is represented by the definite integral ∫012v(t)dt.
(a) Describe the physical meaning of ∫012v(t)dt.
(b) Explain what 121∫012v(t)dt measures and include its units.
(c) Discuss the effect of v(t) changing sign within the interval on the interpretations from parts (a) and (b).