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

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To avoid a collision with the sports car, the minimum deceleration required for your car must be calculated based on initial speeds and acceleration. The sports car is traveling at 11.111 m/s and accelerating at 1 m/s², while your car is initially at 27.777 m/s and starts decelerating from a distance of 100 meters behind. The equations of motion for both vehicles can be set up to find the time and distance needed to ensure no collision occurs. By solving these equations, the necessary deceleration can be determined. This problem highlights the importance of understanding relative motion and kinematics in emergency driving situations.
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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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