An Elementary Treatise On Mechanics for the Use of the Junior Classes At the University ... With a Collection of Examples

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We may arrive at the same results thus by an appli- cation of the principle stated in Art. 40.
A' A p 206 OF UNIFOKMLY ACCELERATED MOTION.
Let the particle be projected from A in direction AP with the velocity u ; — the relative motion of A and P will he the same if we impress upon hoih a velocity equal to u in, the opposite direction ; this reduces P to initial rest, and if P, A be simultaneous positions of the particle and oi A, v their relative velocity at that time t, and A P=s, we have AP=
...\fe AA' = ut (i); .-. s=ut + ^fe.. (ii), and v = u +ft ; the same results as before.
72. Note. The same results might have been arrived at by a process similar to those employed in Art. 69. These we leave as an exercise for the student.
We would here caution him likewise against a loose and incorrect application of the second law of motion to this problem which we have noticed in some works on dynamics.
They state that the space described in consequence of the initial velocity is = ut, and the space that would be described in the same time by the action of the accelerating force y is = \f^, and therefore hy the second law of motion, the whole space described is the sum of these two, or s = m

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