FORT, ACCELERATION, AND VELOCITY DIAGRAMS 289 
~ The acceleration curve is determined in like manner from the velocity 
‘eurve, NQ being made a fixed number of times FH, or, as has been done 
in Fig n Pig. 453, the mid 
ordinate has been g24 C § 
made four times the 29 ay g 
in velocity x, Aa 
for each second! e 6 Dames 4§ 
Conversely, the <8 j2 al: eet ni)) 38 
velocity curve may (8 Velo A be 
_ be determined from ® a Ao NE se 
the acceleration 4 Ri La 
curve, and the space Ss +474 0% 
curve from the = ° 24 6 EN iz whi 
_ velocity curve, be- Time in seconds. ; ay 
_ ginning in each case 4 
at the zero point. _ 453. 
The student agli 
should work out the foregoing example carefully to, say,-the following 
scales :—Time, 1 inch to 2 seconds; space, 1 inch to 50 feet; velocity, 
1 inch to 5 feet per second ; and acceleration, 1 inch to 1 foot per second 
per second. 
The properties of the curves on a time base which have been made 
use of in the foregoing example are applied in a slightly different manner 
in Fig. 454. Suppose the velocity curve to be given. Divide the diagram 
into vertical strips 
A, B, ©, ete., and ; P 
draw the mid ordi- 
nates shown by 
dotted lines. Pro- 
ject the mid ordi- 
nate points of the 
velocity curve on to 
the vertical through 
©, thus obtaining 
the points a, b, ¢, 
ete. Choose a pole Ok Ak Bk Ce D 
P on the time base, é a ie pear EMAC: = 
and join P to a, b, Fig. 454. 
¢, etc. Starting at 
O, draw across the strips A, B, C, ete., continuous lines parallel to Pa, 
Pb, Pe, ete., respectively ; a fair curve through the junctions of these 
lines will be the space-time curve. 
Choose a pole P, on the time base, and draw P,a,, Pidy, P,¢,, ete., 
parallel to the portions of the velocity curve across the strips A, B, C, etc., 
respectively, to meet the vertical line through O at a,, 0,, ¢,, etc. Hori- 
zontal lines from a, 4,, ¢,, etc., to cut the mid ordinates of the strips 
A, B, C, ete., respectively, determines points on the acceleration curve. 
The relations between the different scales are found as follows. Let 
the intervai of time A be d¢ seconds, and at the end of that interval let 
the increase in space be 5s feet, and the increase in velocity dv feet per 
second, At the middle of the interval A let the velocity be v feet per 
T 
