Chapter 245*P2.59(a)As we see from the graph, from about −50 s to 50 sAcela is cruising at a constant positive velocity inthe +xdirection. From 50 s to 200 s, Acelaaccelerates in the +xdirection reaching a top speedof about 170 mi/h. Around 200 s, the engineerapplies the brakes, and the train, still traveling inthe +xdirection, slows down and then stops at350 s. Just after 350 s, Acela reverses direction (vbecomes negative) and steadily gains speed in the−xdirection.t(s)100 200 300–100100200400∆v∆t–5000FIG. P2.59(a)(b)The peak acceleration between 45 and 170 mi/h is given by the slope of the steepest tangentto the vversus tcurve in this interval. From the tangent line shown, we findavt===−()−slopemi hsmi h sm s2∆∆155451005022098..af.(c)Let us use the fact that the area under the
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