Dynamics- collision of cars problem

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SUMMARY

The discussion centers on a collision problem involving two cars, A and B, both initially traveling at 98 ft/s. Car B begins to decelerate at 20 ft/s² after noticing an accident, reducing its speed to 78 ft/s while the distance between the cars decreases to 22.5 ft. Car A, upon noticing the situation, takes 0.5 seconds to apply brakes, decelerating at 30 ft/s². The key question is determining the time of collision and the relative speed at impact.

PREREQUISITES
  • Understanding of kinematics, specifically equations of motion.
  • Familiarity with concepts of acceleration and deceleration.
  • Knowledge of relative velocity calculations.
  • Basic grasp of time-distance-speed relationships.
NEXT STEPS
  • Study kinematic equations for uniformly accelerated motion.
  • Learn how to calculate relative velocity in collision scenarios.
  • Explore advanced braking distance calculations for vehicles.
  • Investigate real-world applications of collision physics in automotive safety.
USEFUL FOR

Students in physics, automotive engineers, and professionals involved in accident reconstruction or vehicle safety analysis will benefit from this discussion.

chiraganand
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The problem is like this
Assume both cars A and B are intially traveling to the right at 98 ft/s. Car A is tailgating leaving very little room between car A and car B. At that instant driver of car B notices a n accident and starts to break witha deceleration of 2o ft/s^2. By the time the driver of car A notices the distance betwwen them has reduced to 22.5 ft and the velocity of car B is slowed down to 78 ft/s. Assume that the driver of car A immediately puts the brakes and it takes him only 0.5 s to apply breaks. The car decelerates with 30 ft/s^2. Calculate when collision occurs and relative speed of collision.

I have already solved the problem. attaching the solution. can anyone let me know if i am correct or wrong
 

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chiraganand said:
The problem is like this
Assume that the driver of car A immediately puts the brakes and it takes him only 0.5 s to apply brakes. /QUOTE]

Which is it? Does he immediately apply the brakes or does it take him 0.5s to apply the brakes?
 
He applies the break after 0.5 s
 

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