A car starts from rest at a stop sign. It accelerates at 4.0 m/s2 for 9 seconds, coasts for 6 s, and then slows down at a rate of 3.0 m/s2 for the next stop sign. How far apart are the stop signs?
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I hope it actually stops, not just slows down.
Speed after 9 secs = (at) = 4 x 9, = 36m/sec.
Distance covered during this phase = (v^2/2a) = 162 metres.
Distance coasting = (36 x 6) = 216 metres.
The car brakes. Distance required = (v^2/2a), = 36^2/6, = 216 metres.
Distance between stop signs = (216 + 216 + 162) = 594 metres.
Speed after 9 secs = (at) = 4 x 9, = 36m/sec.
Distance covered during this phase = (v^2/2a) = 162 metres.
Distance coasting = (36 x 6) = 216 metres.
The car brakes. Distance required = (v^2/2a), = 36^2/6, = 216 metres.
Distance between stop signs = (216 + 216 + 162) = 594 metres.