Minimum Car Deceleration to Avoid Collision: Solving a Confusing Highway Problem

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SUMMARY

The discussion revolves around calculating the minimum deceleration required for a car traveling at 27.777 m/s (100 km/h) to avoid colliding with a sports car accelerating at 1 m/s² from an initial speed of 11.111 m/s (40 km/h). The scenario specifies that the distance between the two vehicles is 100 meters when the braking begins. By applying the equations of motion, the necessary deceleration can be determined to ensure a safe stop before reaching the sports car.

PREREQUISITES
  • Understanding of kinematic equations for uniformly accelerated motion
  • Basic knowledge of physics concepts such as velocity, acceleration, and distance
  • Ability to manipulate algebraic equations to solve for unknowns
  • Familiarity with units of measurement in the metric system
NEXT STEPS
  • Study the kinematic equations of motion in detail
  • Learn how to apply these equations to real-world collision avoidance scenarios
  • Explore the impact of different deceleration rates on stopping distances
  • Investigate advanced topics such as braking distance calculations in varying conditions
USEFUL FOR

This discussion is beneficial for automotive engineers, physics students, and anyone interested in vehicle dynamics and safety measures in collision avoidance scenarios.

MrRottenTreats
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Question: You happen to be the one driving down the Highway that this person pulls in front of. You prepare to make a fast lane switch but are boxed in by a transport truck in the fast lane. Thus, you step on the brake pedal. You are traveling 27.777 .. m/s (100 km/h) and are 100 m behind the sports car when you begin to decelerate. The sports car is traveling 11.111 .. m/s (40 km/h) and is accelerating at 1 m/s^2. Solve for the minimum value of deceleration required by your car to just barely avoid a collision with the sports car.

i don't really know what to do.. i tried drawing a diagram to help, but its not working out for me, interpreting it.
 
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did u try it yet
 
yea, i got the sports car being:
v1 = 11.111 .. m/s
a = 1 m/s^2
d = d
t = t (same for both)

your car
v1 = 27.77 .. m/s
d = d - 100
t = t
a = ?
 

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