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Consider the following one-dimensional motion. A race car starts from rest and speeds up to 100 m/s. Which of the following statements are true?

(1) The average velocity is zero

(2) The average velocity is 100 m/s

(3) At no point does the average velocity equal the instantaneous velocity

(4) The average velocity = instantaneous velocity only when the car starts from rest

(1) and (2): The car’s average velocity cannot be evaluated unambiguously with the information given, but it must be some value between 0 and 100 m/s. So we cant say for sure its (1) or (2).
(3) is false also: Because the car will have every instantaneous velocity between 0 and 100 m/s at some time during the interval, there must be some instant at which the instantaneous velocity is equal to the average velocity.
(4): We can't say for sure that these two values are equal only at the beginning of the event.
edited Aug 11, 2014