Determine whether the following statements are true and give an explanation or counterexample.
c. It is impossible for the instantaneous velocity at all times a≤t≤b to equal the average velocity over the interval a≤t≤b.

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1. Understand the definitions of instantaneous velocity and average velocity. Instantaneous velocity is the velocity of an object at a specific moment in time, while average velocity is the total displacement divided by the total time over an interval.
2. Recall the formula for average velocity over the interval [a, b]: it is given by \( v_{avg} = \frac{s(b) - s(a)}{b - a} \), where \( s(t) \) is the position function.
3. Recognize that instantaneous velocity at a point \( t \) is defined as the derivative of the position function: \( v_{inst}(t) = s'(t) \).
4. Consider the Mean Value Theorem, which states that if a function is continuous on [a, b] and differentiable on (a, b), then there exists at least one point \( c \) in (a, b) such that \( s'(c) = v_{avg} \).
5. Conclude that it is possible for the instantaneous velocity at some point in the interval to equal the average velocity, thus the statement is false. Provide a counterexample, such as a linear function where the instantaneous and average velocities are equal at all points.