Calculating Minimum Stopping Distance for a Car at Different Speeds

[klm]

The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the distance traveled during the drivers reaction time of 0.560 s.
what is the min. stopping distance for the same car traveling at a speed of 38.0 m/s?

tried to use this equation v^2 - u^2 = 2 a s
but then didnt know what to do.

 

[Doc Al]

Use that equation to figure out the car's acceleration. What distance did you use? (How far has the car traveled before the brakes are applied?)

 

[klm]

43.2m is the real distance he first travels with the velocity of 30 m/s. because i subtracted 16.8 m from the 60 m.
so my a= 10.416

 

[Doc Al]

Good! Now apply that--in reverse--to the second case, where the speed is 38 m/s, to find the new total stopping distance. (You'll have to calculate a new "reaction time distance".) The car's acceleration remains the same.

 

[klm]

i don't know how to find a new reaction time distance??
i used this formula :
0^2 - 38^2 = 2(10.416) x
and found x to be 69.3m but this is incorrect. can you please help me.

 

[Doc Al]

i don't know how to find a new reaction time distance??

Do it the same way as before. How far does the car move before the brakes are applied?

 

[klm]

38 x .56?
=21.28 m
but what do i do with that?

 

[Doc Al]

You add it to the other distance. Understand what happens when the person wants to stop: (1) there's a time delay due to reaction time, so the car moves some distance before the brakes are even applied; (2) once the brakes are applied, the car accelerates to a stop.

The total stopping distance is the sum of both of these distances.

 

[klm]

you add 21.28 to 60? to get 81.28m?

 

[Doc Al]

you add 21.28 to 60? to get 81.28m?

No. 60m was the total stopping distance for the 30m/s case--nothing to do with the 38 m/s case!

Add 21.28 m to the distance you calculated for the de-accelerating phase of the motion.

 

[klm]

to the 69.3?
69.3+21.28 = 90.58?
sorry if i leave really quick i have to run to class in about 2 mins!

 

[Doc Al]

Yes.

 

[klm]

THANK YOU! so so much