Calculating Min Stopping Distance for Car Traveling at 60 m/s

[Phoenixtears]

Homework Statement

The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the distance traveled during the driver's reaction time of 0.50 s.

(a) What is the minimum stopping distance for the same car traveling at a speed of 60 m/s?
m

Homework Equations

Vf^2= V0^2 + 2ax

The Attempt at a Solution

Now I have my equation set up, but I can't figure out the change in x. Instead I have (60m-x) in my equation, but I'm looking for acceleration so that I can use that in my next equation when it comes to going 60 m/s. How is one to find the other x if it is not given?

~Phoenix

 

[Dschumanji]

The relevant equation should be written as:

V_f² = V_i² +2a$$\Delta$$x

$$\Delta$$x is the distance the car goes to stop.

 

[Phoenixtears]

Gotcha... wow, now I feel rather dense. That makes perfect sense- I've no idea why I skipped over that. All right, I worked the equations and got 7.5 m/s/s as my acceleration. I used that in my equation involving 60 m/s (0^2= 60^2 + 2(7.5)x) and got 240 as my answer. Yet this is wrong, is there something in my calculations that is incorrect?

 

[Dschumanji]

Did you include the distance you travel before you hit the brakes?

 

[Phoenixtears]

Yes, using the equation: deltax= V0*t + (.5)(a)(t^2). My numbers being: V0=60; t=.5; a=7.5. totalling to 270.94, and yet that did not work either.

(I had tried both answers before)

 

[Dschumanji]

Yes, using the equation: deltax= V0*t + (.5)(a)(t^2). My numbers being: V0=60; t=.5; a=7.5. totalling to 270.94, and yet that did not work either.

(I had tried both answers before)

The car is not accelerating before the brakes are applied.

The equation you should use is x = vt.

 

[Phoenixtears]

Yikes. That's just basic... I think I'm a bit tired. Right, well then, that would mean it travel 60m*.5s leaving 120m total during that time. Adding that to my original 240 brings me to 270m total... well. That was just depressing, as that didn't work. :/ Now something must be wrong. I've done everything wrong along the way, then correcting it, and yet 270 seems as if that is correct...

 

[Dschumanji]

Is the correct answer 210m?