Calculating Minimum Trailing Distance in a Reaction Time Scenario

[Argento7]

Hello,

Homework Statement

You are driving along the New York State Thruway in a line of cars all traveling at a constant speed of 108.1 km/hr (Which I converted to 30.02 m/s). The car in front of you applies its brakes for maximum acceleration. You then apply your brakes to achieve the same maximum acceleration after only a 1 s delay due to reaction time. What distance behind the car in front of you must you be to avoid a collision?

Homework Equations

How can I factor in the 1s delay on the time?

All the equations for the problem are located here:
http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L6a1.gif

The Attempt at a Solution

I set the origin and my initial position to 0 for the car in front of you. I also had tried several times to figure out the acceleration.

 

[LowlyPion]

Hello,

Homework Statement

You are driving along the New York State Thruway in a line of cars all traveling at a constant speed of 108.1 km/hr (Which I converted to 30.02 m/s). The car in front of you applies its brakes for maximum acceleration. You then apply your brakes to achieve the same maximum acceleration after only a 1 s delay due to reaction time. What distance behind the car in front of you must you be to avoid a collision?

Homework Equations

How can I factor in the 1s delay on the time?

All the equations for the problem are located here:
http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L6a1.gif

The Attempt at a Solution

I set the origin and my initial position to 0 for the car in front of you. I also had tried several times to figure out the acceleration.

Welcome to PF.

Hint: You don't need to know actual acceleration. Just that it is the same and yours is 1 s later.

If you plotted a graph of velocity for each car they will look the same ... except for the 1 sec delay. So long as you start deceleration before you reach the point on the road that the car ahead starts then you should maintain the same distance to stopping.

For a 1 second margin then how does that translate into distance?

 

[Kasper_NYC]

Hi, you were traveling at 30.02m/s, so in 1 second you will cover 30.02m, and you need 1 second to react. So at least you have to be a 30.02 meters distance from the car that is ahead of you.

 

[LowlyPion]

Hi, you were traveling at 30.02m/s, so in 1 second you will cover 30.02m, and you need 1 second to react. So at least you have to be a 30.02 meters distance from the car that is ahead of you.

There you go. You're ready to drive safely.

 

[Argento7]

Thank you both so much