6 BEST AND MOTION 



Construct a parallelogram AB CD such that the two sides AB, AD 

 which meet in A represent the two motions x, y to be compounded, 

 as regards both magnitude and direction; then the diagonal AC 

 which passes through A will represent the resultant obtained by 

 compounding these two motions. 



VELOCITY 



8. Uniform and variable velocity. Velocity means simply 

 rate bf motion. It may be either uniform or variable. If a point 

 moves in such a way that a feet are described in each second of 

 its motion, no matter which second we select, we say that the 

 velocity of the pgint is a uniform velocity of a feet per second. 

 If, however, the point moves 'a feet in one second, b feet in another, 

 c feet in a third, and so on, we cannot say that any one of the 

 quantities a, b, or c measures the velocity. The velocity is now 

 said to be variable : it is different at different stages of the motion. 

 To define the velocity at any instant, we take an infinitesimal in- 

 terval of time dt and measure the distance ds described in this 



ds 



tune. We then define the ratio to be the velocity at the instant 



dt 



ds 



at which the interval dt is taken. If the velocity is uniform, 



dt 



is the space described in unit time, and so the present definition 

 of velocity becomes the same as that already given. 



Average velocity. If a point moves with variable velocity, and 



describes a distance of a feet in t seconds, we speak of - as the 



t 



" average velocity " of the moving point during the time t. This 

 average velocity is the velocity which would have to be possessed 

 by an imaginary point moving with uniform velocity, if it were to 

 cover the same distance in time t as the actual point moving with 

 variable velocity. 



Units. In measuring a velocity we need to speak in terms of a 

 unit of length and of a unit of tune ; for instance, in saying that 

 a point has a velocity of a feet per second we have selected the foot 



