DYNAMICS. 



Of Motion uniformly accelerated. 



262. A body, perfectly free, having once received an impulse 

 will continue its motion, the velocity and the direction remaining 

 always the same as at the first instant. But if it receive a new 

 impulse in the same direction, or in a direction opposite to the 

 first, it will move with a velocity equal in the former case to the 

 sum, and in the latter to the difference of the velocities it has 

 successively received. 



Hence, if we suppose that, at determinate intervals of time, 

 the body receives new impulses in the same direction, or in a 

 direction opposite to the first, it will have a varied or unequal 

 motion, and its velocity will change or become different at the 

 commencement of each interval of time. 



Whatever this may be, the velocity of a body at the end of 

 any given period of time, is to be estimated by the space which 

 this body is capable of describing in a unit of time, on the sup- 

 position that its motion becomes uniform at the instant from 

 which this velocity is to be reckoned. 



Any force, which acting upon a body causes it to vary its 

 motion, is called an accelerating or retarding force. When it acts 

 equally at equal intervals of time, it is' called a uniformly accelerat- 

 ing, or uniformly retarding force, according as it tends to increase 

 or diminish the actual velocity of the body. 



We shall now examine the circumstances of motion uniform- 

 ly accelerated. 



263. Since in this kind of motion, the accelerating force acts 

 always in the same manner, if we suppose that u is the velocity 



