Question

Which of the following options represents the speed (S) an object falls after 3 seconds if the speed is 49.0 m/s after 5 seconds, given that the speed (S) varies directly with time?

A) S = 81.6 m/s
B) S = 29.4 m/s
C) S = 3.3 m/s
D) S = 16.3 m/s

Answer 1

To find the speed after 3 seconds when given the speed at 5 seconds, with speed varying directly with time, we use the direct variation principle. The constant of variation is determined using the given values and then applied to find the speed at the requested time. The correct answer is B) S = 29.4 m/s.

Step-by-step explanation:

The student asked which option represents the speed (S) an object falls after 3 seconds, if the speed is 49.0 m/s after 5 seconds, assuming that speed varies directly with time. If speed varies directly with time, the speed at which an object is falling at 5 seconds (49.0 m/s) can be used to determine the speed after 3 seconds using the direct variation equation S = kt, where S is the speed, k is the constant of variation, and t is the time.

First, we find the constant k using the information provided: S = kt becomes 49.0 m/s = k × 5 s, so k = 49.0 m/s / 5 s = 9.8 m/s2.

Then we calculate the speed after 3 seconds: S = kt becomes S = 9.8 m/s2 × 3 s, yielding S = 29.4 m/s. Thus, the correct answer is option B) S = 29.4 m/s.