Example 30.9. A locomotive draws a train of mass 400 tonnes, including its own mass, a a level ground with a uniform acceleration, until it acquires a velocity of 54 km. p.h in 5 minutes. If the frictional resistance is 40 newtons per tonne of mass and the air resistance varie with the square of the velocity, find the power of the engine. Take air resistance as 500 newtons at 18 km. p.h.

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