Question

2.4 velocity vs. time graphs

1. identify the time, or times, at which the instantaneous velocity is greatest, and the time, or times, at which it is negative. a sketch of velocity vs. time derived from the figure will aid in arriving at the correct answers.

a. the instantaneous velocity is greatest at f, and it is negative at d, h, l, j, and k.
b. the instantaneous velocity is greatest at e, and it is negative at a, b, and f.
c. the instantaneous velocity is greatest at f, and it is negative at d, h, l, j, and k
d. the instantaneous velocity is greatest at d, and it is negative at a, b, and f.

Explanation:

Step1: Recall velocity - position relationship

Instantaneous velocity is the slope of the position - time graph.

Step2: Analyze where slope is maximum

The steeper the slope of the position - time graph, the greater the magnitude of the instantaneous velocity. At point f, the slope of the position - time graph is the steepest (in terms of magnitude), so the instantaneous velocity is greatest at f.

Step3: Determine when velocity is negative

Velocity is negative when the slope of the position - time graph is negative. The slope is negative at points a, b, and f (the position is decreasing with time at these points).

Answer:

B. The instantaneous velocity is greatest at e, and it is negative at a, b, and f. (There is a typo in the explanations above, it should be greatest at f. Among the options, the correct one based on the slope - analysis is the one where greatest velocity is at f and negative at a, b, f which is option B after correcting the 'e' to 'f' in the option description)