Help with Formula: Minimum Dist. to Avoid Hitting Car in Front

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To determine the minimum distance to avoid hitting the car in front, calculate the distance the leading car travels during the 2.4 seconds before the following car applies its brakes. The equation involves the initial speed of both cars at 80 km/h and the unknown acceleration of the leading car. After 2.4 seconds, the following car also applies brakes at maximum acceleration, which must be factored into the distance calculation. The final expression will include the variable for acceleration, allowing for the calculation of the necessary distance to prevent a collision. Understanding these dynamics is crucial for solving the problem effectively.
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Homework Statement


you are driving behind another car on the highway and both of you are going at a constant 80 km/h. the car in front of you slams on the brakes suddenly at max acceleration. 2.4 seconds later you apply your brakes (also at max acceleration). what is the minimum distance you can be away to avoid hitting the car in front of you?


Homework Equations



not sure..need help on this one..

The Attempt at a Solution


known information
V1 = 80km/h
v2 = 80 km/h
t1 = 0 s
t2 = 2.4 s
d = ?
 
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Hi dance_4dance, welcome to PF.

From the instant that the brakes are applied, how far will the car in front travel before it stops? Assume that the acceleration is the variable a. The result will be an expression that contains that variable.
 

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