Intermediate physics / by W. Watson.

  • Watson, W. (William), 1868-1919.
Date:
1912
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Licence: In copyright

Credit: Intermediate physics / by W. Watson. Source: Wellcome Collection.

Provider: This material has been provided by UCL Library Services. The original may be consulted at UCL (University College London)

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    can be made as small as we please, while the true space traversed is always intermediate between those corresponding to the two stepped curves. Hence if the number of steps is very great both the stepped curves practically coin- cide with the actual velocity curve oPjPgPg, &c., and the actual space traversed in any interval is represented numeri- cally by the area included between the velocity curve, the axis of time, and the ordinates drawn through the points cor- responding to the commence- ment and end of the interval considered. Let us now proceed to interpret what is the nature of the motion of a body for which the velocity curve is the straight line pp' (Fig. 6). In the first place the body at the instant when we ygiQ(.i^y. start to reckon time is moving with a speed represented curve for by OP, which we will call Vq. Further, the speed is uniform obviously increasing, and if M^, M^, Mg represent times of 1 second, 2 seconds, and 3 seconds from the start, the increase in the sp6ed during the first second is p^q^ the increase during the second second is P2Q2, and that during the third second is P3Q3. Now since om^ ^ MjM2 = M^Mg, each representing 1 second, pq^ = p^q^ = PgQg. But the triangles pp^Qi, ^iP2^2^ Vs^s similar. Therefore, acceleration. and hence P^i ^1^2 FM^' That is, the increase of speed during each second is the same, or in other words, the acceleration is constant. Hence we conclude that the velocity curve pp' represents the motion of a body which starts with a speed Vq represented by op, and moves with a uniform acceleration represented by p^q^. If m' represents a time t from the start, then np' is equal to at, where a is the acceleration, for the speed will have ^^^^^ ^^.^ increased by at in t seconds. The space traversed by versed when the body in the time t is represented by the area of acceleration the figure opp'm', that is by the sum of the figures is uniform. opnm' and pp'n. But the area of opnm' is equal to op x om', that is 7;^^,