When a highspeed passenger train traveling at 161 km/h rounds a bend, the engineer is shocked to
see that a locomotive has improperly entered onto the track from a siding and is a distance D = 676
m ahead (Fig. ). The locomotive is moving at 29.0km/h. The engineer of the highspeed train
immediately applies the brakes, (a) What must be the magnitude of the resulting constant
deceleration if a collision is to be just avoided? (b) Assume that the engineer is at x = 0 when, at t
=
0, he first spots the locomotive. Sketch the
x
(t) curves representing the locomotive and highspeed
train for the situations in which a collision is just avoided and is not quite avoided.
Fig.
Sol.
In this solution we elect to wait until the last step to convert to SI units. We start with Eq.
x – x
0
= ½ (v
0
+ v)t
and denote the train’s initial velocity as
v
t
and the locomotive’s velocity as
v
(which is also the final velocity of the train, if the rearend collision is barely avoided). We note that
the distance ∆
x
consists of the original gap between them
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 Spring '10
 abraham
 1km, highspeed train, highspeed passenger train, 0.676km, 29.0km/h

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