Final answer:
The instantaneous velocity of the pebble after 3 seconds can be estimated by using the equation v(t) = 3.0 + 1.5t² m/s. After calculating and converting to feet per second, the closest answer from the choices given is 48 ft/s, even though the calculated value is approximately 54.1385 ft/s.
Step-by-step explanation:
To estimate the instantaneous velocity of a pebble after 3 seconds, we can use the provided velocity-time equation, which seems to be v(t) = 3.0 + 1.5t² m/s. To find the instantaneous velocity at 3 seconds (t = 3 s), we substitute 3 for t in the equation:
v(3 s) = 3.0 + 1.5(3)²
v(3 s) = 3.0 + 1.5(9)
v(3 s) = 3.0 + 13.5
v(3 s) = 16.5 m/s
To convert meters per second to feet per second, we use the conversion factor, 1 m/s ≈ 3.281 ft/s. Therefore, the instantaneous velocity in feet per second is:
16.5 m/s × 3.281 ft/s = 54.1385 ft/s
This value is not listed among the answer choices, which suggests either there is an error in the question or the choices provided. However, based on the options given, option A, 48 ft/s, is the closest to the calculated value.