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

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In summary, the problem presents a scenario where two cars are traveling at a constant speed of 80 km/h on a highway, with the car in front suddenly braking at max acceleration. The question asks for the minimum distance needed for the car behind to avoid a collision, assuming it also brakes at max acceleration 2.4 seconds later. Using known information such as the initial velocities and time, we can set up an expression to determine the distance traveled by the car in front before coming to a stop.
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dance_4dance
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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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  • #2
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.
 

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

1. What is the formula for calculating the minimum distance to avoid hitting a car in front?

The formula for calculating the minimum distance to avoid hitting a car in front is: minimum distance = (speed of your car * reaction time) + (speed of your car)^2 / (2 * deceleration)

2. How do I determine my reaction time for this formula?

Your reaction time can vary, but on average it is about 0.75 seconds. However, it is recommended to use a higher value, such as 1 second, to account for unexpected distractions or delays in reaction time.

3. What units should be used for the speed and deceleration values in the formula?

The speed values should be in meters per second (m/s) and the deceleration value should be in meters per second squared (m/s^2).

4. Can this formula be applied to any type of vehicle?

Yes, this formula can be applied to any type of vehicle as long as the speed and deceleration values are converted to the appropriate units.

5. How accurate is this formula in determining the minimum distance to avoid a collision?

This formula provides a good estimate for the minimum distance needed to avoid a collision, but it is important to note that other factors such as weather conditions, road conditions, and driver behavior can also affect the distance needed to safely stop a vehicle.

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