Given that the physical quantities s, v,a, and t have dimensions[s]= L, [v]= LT-1,[a] = LT-2, and [t] = T. Determine whether each of the following equations is
dimensionally consistent:
(a) s = vt + 1/2at²
(b) s = vt² + 1/2 at
(c) v = sin(at² /s).
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Asilver dollar is dropped from the top of a building that is 1324 feet tall. use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) determine the position and velocity functions for the coin. s(t) = v(t) = (b) determine the average velocity on the interval [1, 2]. ft/s (c) find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) find the time required for the coin to reach the ground level. (round your answer to three decimal places.) t = s (e) find the velocity of the coin at impact. (round your answer to three decimal places.) ft/s