Solve Collision Question: Will Sue's Car Hit the Van?

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Speedy Sue, traveling at 32.0 m/s, enters a tunnel where a van is 160 m ahead, moving at 5.20 m/s. With a braking acceleration of -2.00 m/s², calculations show that a collision will occur. To determine the collision point, it's essential to calculate how far Sue travels while braking and the time it takes to stop. The final position function can be used to find the distance Sue covers before stopping, as well as the distance the van travels during that time. The discussion emphasizes the need for precise calculations to find the exact point of collision in the tunnel.
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collision question!

Speedy Sue, driving at 32.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 160 m ahead traveling with velocity 5.20 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's car and the van and enter zero for the time.




i already know there will be a collision
but I am not sure how to calculate how far into the tunnel it will happen

im guessin to use the final position function..but i dunno
 
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If Sue starts braking immediately after entering the tunnel, how far into the tunnel will she have come to a stop?
How long will it take her to brake? What is then the distance the van has travelled?
 

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