. The Ontario high school physics. ocity x time;hence if s represents space, s = ^ at X t = h at ^ext, let the initial velocity be u cm. per sec. Then we have:Initial velocity = ii cm. per n = u + at cm. per sec. Average n = | (u + u + at) cm. per sec. = w + |- at II II Then space s = average velocity x time = {it + ^ at) t = ut + ^ at^ cm. In this expression note that nt expresses the space which wouldbe traversed in time t with a uniform velocity ii, and ^^> «<- is thespace passed over when the initial velocity = 0. The entire spaceis then the sum of these. 22 DISPLACEMEN
. The Ontario high school physics. ocity x time;hence if s represents space, s = ^ at X t = h at ^ext, let the initial velocity be u cm. per sec. Then we have:Initial velocity = ii cm. per n = u + at cm. per sec. Average n = | (u + u + at) cm. per sec. = w + |- at II II Then space s = average velocity x time = {it + ^ at) t = ut + ^ at^ cm. In this expression note that nt expresses the space which wouldbe traversed in time t with a uniform velocity ii, and ^^> «<- is thespace passed over when the initial velocity = 0. The entire spaceis then the sum of these. 22 DISPLACEMENT, VELOCITY, ACCELERATION 27. Graphical Representation. The relations between velocity,acceleration, space and time in uniformly accelerated motion can beshown by a geometrical figure. Let distance from 0along the horizontal lineOX represent time in se-conds, OR representing tseconds, OL one half of thisor ^t seconds. Vertical linesrepresent velocities. Thevelocity at the beginning7t, is represented by OM;that at the end of t se-. «o i ^ Time in seconds Fig. 15.—Space traversed can be represented by an area. i i_ ti d i ^ ^ • conds by EF; and so on. At the middle of the time the velocity is LQ. The velocity at the beginning is ^i — OM. At the end of tseconds it is u + at = RP. Hence NP = at. The mean velocityis w + \ at — LQ. If the velocity is uniform (without acceleration), the space tra-versed is tit. Now in the figure, u = OM and t = OR, Hence vt = OM x OR = area of rectangle MR, and the spacetraversed is represented by the area of the rectangle. Again with accelerated motion the space traversed is (tt + ^ at) X t = tit + ^ at-, But tit = area of rectangle MR, and ^at = « triangle MNP. Hence the space traversed is represented by the area of the figureOMPR. 28. Motion under Gravity. The most familiar illustration ofmotion with uniform acceleration is a body falling freely. Supposea stone to be dropped from a height. At once it acquires a velocitydownwards, Avhich
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