Consider the following one-dimensional motions: (A) A ball thrown directly upward rises to a highest point and falls back into the thrower’s hand. (B) A race car starts from rest and speeds up to 100 m/s. (C) A spacecraft drifts through space at constant velocity. Are there any points in the motion

Question

Consider the following one-dimensional motions: (A) A ball thrown directly upward rises to a highest point and falls back into the thrower’s hand. (B) A race car starts from rest and speeds up to 100 m/s. (C) A spacecraft drifts through space at constant velocity. Are there any points in the motion of these objects at which the instantaneous velocity has the same value as the average velocity over the entire motion? If so, identify the point(s).

Accepted Answer

(A) The average velocity for the thrown ball is zero because the ball returns to the starting point; thus its displacement is zero. (Remember that average velocity is defined as Δx/Δt.) There is one point at which the instantaneous velocity is zero—at the top of the motion.

(B) 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. 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.

(C) Because the spacecraft’s instantaneous velocity is constant, its instantaneous velocity at any time and its average velocity over any time interval are the same.

Question 2.2: Consider the following one-dimensional motions: (A) A ball t...

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