Finding maximum reaction time to avoid collision at 18.0 m/s

[elizabethg]

Hello, I need help on this problem...

A car is traveling at a constant speed of 18.0 m/s, when the motorist sees a cow in the road 38.0 m ahead. If the maximum acceleration of the vehicle is -4.50 m/s^2, what is the maximum reaction time fo the motorist that will allow her to avoid hitting the cow?

I have tried many different ways. I was thinking you would use an integral from 0 to x because you want to find the maximum reaction time. The equation I thought to integrate was -38+18t+.5(-4.5)t^2 which, of course, was wrong. Please help!

 

[PureEnergy]

The motorist must stop within a time of 38/18, since this is how long it will take her to cover 38 meters. The minimum time it will take her to stop occurs when she deaccelerates at a constant -4.50 until the car stops. The maximum reaction time will be the difference of these two times. Using your numbers, I find that her minimum stop time exceeds the time she is allotted (38/18). Are you sure all the values are correct?

 

[elizabethg]

All my values are correct, but i thought you would integrate it or something, the answers our teacher gave us to choose from were .0251, .111, .360, .521, .684. i thought you would just plug those numbers in. I am not really sure.

 

[PureEnergy]

I believe my method is correct and see no reason for integration (assuming you already have the derived basic kinematic equations). I suspect one of your given values is incorrect. It's possible the teacher may have made a mistake for one of the numbers.

 

[jdstokes]

All my values are correct, but i thought you would integrate it or something, the answers our teacher gave us to choose from were .0251, .111, .360, .521, .684. i thought you would just plug those numbers in. I am not really sure.

If the car decelerates uniformly from 18.0 ms^-2 to 0 ms^-2 it will cover a distance of $\Delta x=\frac{v^2 - u^2}{2a}$ or 36 m. That means the car may travel an allowable distance of 2 m before the driver hits the brakes. Therefore, at a velocity of 18 ms^-1, the allowable reaction time is 0.111 s.

 

[elizabethg]

thank you, but i figured it out already, it just took me some time, i truly appreciate it from the bottom of my heart that you would take your time to help me. thank you