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

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SUMMARY

The discussion focuses on calculating the minimum distance required to avoid a collision when driving behind another car. Both vehicles are traveling at a speed of 80 km/h, with the car in front applying brakes suddenly, followed by the second car after a delay of 2.4 seconds. The solution involves determining the distance the first car travels during its deceleration, which is dependent on the variable acceleration (a). The key equations for motion under constant acceleration are essential for deriving the required distance.

PREREQUISITES
  • Understanding of kinematic equations for constant acceleration
  • Basic knowledge of speed, distance, and time relationships
  • Familiarity with the concept of relative motion
  • Ability to manipulate algebraic expressions involving variables
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  • Study kinematic equations, particularly those involving acceleration and deceleration
  • Learn how to calculate stopping distances based on initial speed and acceleration
  • Research the effects of reaction time on stopping distances in driving scenarios
  • Explore real-world applications of physics in automotive safety and collision avoidance
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This discussion is beneficial for students studying physics, particularly in the context of motion and forces, as well as for drivers interested in understanding safe following distances and braking dynamics.

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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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