William Anthony Granville

“ Our notion of velocity tells us at once that (C) does not give us the actual velocity at the end of two seconds; for even if we take very small, say or of a second, (C) still gives only the average velocity during the corresponding small interval of time. But what we do mean by the velocity at the end of two seconds is the limit of the average velocity when diminishes towards zero ”

“ By experiment it has been found that a body falling freely from rest in a vacuum near the earth's surface follows approximately the law , where s = space (height) in feet, t = time in seconds. Find the velocity and acceleration (a) at any instant; (b) at end of the first second; (c) at end of the fifth second.
which tells us that the acceleration of a falling body is constant; in other words, the velocity increases 32.2 ft. per sec. every second it keeps on falling. ”

“ The acceleration is the derivative of the velocity with respect to the time.
73. Component accelerations. Curvilinear motion. In treatises on Mechanics it is shown that in curvilinear motion the acceleration is not, like the velocity, directed along the tangent, but toward the concave side, of the path of motion. ”