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

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SUMMARY

In the collision scenario involving Speedy Sue and a van, Sue's car, traveling at 32.0 m/s, will collide with the van, which is 160 m ahead and moving at 5.20 m/s. Sue's braking acceleration is -2.00 m/s². Calculations reveal that the collision occurs after Sue travels a specific distance into the tunnel, which can be determined using kinematic equations. The exact distance and time of the collision can be calculated by applying the final position function and analyzing both vehicles' motion.

PREREQUISITES
  • Kinematic equations for uniformly accelerated motion
  • Understanding of relative velocity concepts
  • Basic algebra for solving equations
  • Knowledge of braking distance calculations
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  • Calculate the stopping distance for Speedy Sue's car using the formula: d = v² / (2 * a)
  • Learn how to apply the relative motion concept to determine collision points
  • Explore the use of kinematic equations to analyze motion in one dimension
  • Study the implications of different braking accelerations on collision outcomes
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Physics students, automotive engineers, and anyone interested in understanding vehicle dynamics and collision analysis.

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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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