What Is the Correct Formula for Stopping Distance in Physics Homework?

[Coop]

Homework Statement

The driver of a car at 31 m/s sees (t = 0, x = 0) an obstacle down the road and brakes. The car slows down with a constant deceleration which has a magnitude of 6 m/s^2. Select the correct statement below (let d = stopping distance, all units are SI)

a. The position x(t) = 31t + 3t^2
b. The velocity v(t) = 31 - 3t
c. Stopping distance = 961 - 12d
d. The velocity v(t) = d/t
e. None of the above

Homework Equations

Vf = Vi + at
Vf^2 = Vi^2 + 2ad
Xf = Xi + Vi*t + .5at^2

The Attempt at a Solution

a. The position x(t) = 31t + 3t^2

is not correct, because Xf = Xi + Vi*t + .5at^2, so x(t) = 31t - 3t^2

b. The velocity v(t) = 31 - 3t

is not correct, because Vf = Vi + at, so v(t) = 31 - 6t

c. Stopping distance = 961 - 12d

is correct, because Vf^2 = Vi^2 + 2ad, so 0 = 31^2 + 2(-6)d = 961 - 12d => d = 80 m

d. The velocity v(t) = d/t

is correct, because the velocity at time t can solved by dividing the distance traveled over the time taken

But the answer key says c. is correct, why is d. not also correct? Is it because dividing d/t would only give the AVERAGE velocity, not the velocity at time t?

Thanks,
Coop

 

[Doc Al]

Is it because dividing d/t would only give the AVERAGE velocity, not the velocity at time t?

Exactly.

 

[Coop]

Thanks :)

 

[nasu]

c cannot be correct unless you did dot copy it exactly as in the book.

d IS the stopping distance. So c will read
d=961-12*d
which is not true, is it?

 

[Doc Al]

Yes, nasu is correct. Choice c makes no sense. (I didn't read it before, I'm afraid.) Did you copy it correctly?

 

[Coop]

It's from a practice test made by my prof., directly choice c reads "The equation for the stopping distance is 961 - 12d = 0"

 

[Doc Al]

It's from a practice test made by my prof., directly choice c reads "The equation for the stopping distance is 961 - 12d = 0"

That's more like it. (Quite different from what you wrote the first time.)

 

[Coop]

Oh my mistake, I didn't realize, but now that you guys explained it I can see the difference