# Answer to Question #1538 in Mechanics | Relativity for Deep

Question #1538
Speedy Sue, driving at 33.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 175 m ahead traveling with velocity 5.10 m/s. Sue applies her brakes but can accelerate only at -2.00 m/s2 because the road is wet. Will there be a collision?If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sue&#039;s car and the van and enter zero for the time.
1
2011-02-14T06:53:30-0500
According to the equations of the motion,
h = h0 + v0t - at2/2, where h = 175 m, v0 = (33.0-5.1) = 27.9 m/s, a = 2 m/s2, h0 =0
So we have to solve an equation to find the time:
175 = 27.9t - 2t2/2
t2 - 27.9t + 175 =0
D = 8.852
t1 = 18.38 s; t2 = 9.52 s.

We have to use the smallest time of 9.52s. At this time the velocity would be V = V0-at = 27.9 - 2*9.52 = 8.85 m/s, it means that the Sue will not have a zero velocity when she reaches the van - and collision will occure at 9.52 seconds after entering the tunnel.

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