1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Why is the answer half of my answer?

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data
    The driver of a car traveling at 71 ft/sec suddenly applies the brakes. The position of the car is s = 71t - 20t2, t seconds after the driver applies the brakes. After how many seconds does the car come to a stop? Round your answer to the nearest tenth.

    2. Relevant equations

    3. The attempt at a solution
    t=3.55 = 3.6

    However the correct answer is 1.8, which is half my answer, but I do not understand why you would divide by 2? Or where I went wrong?
  2. jcsd
  3. Oct 10, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What made you write this?
  4. Oct 10, 2011 #3
    Well, because the position of the car is represented by the function s=71t-20t2, and since the driver is applying the brakes and coming to a stop, his postion when stopped should be s=0.
  5. Oct 10, 2011 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Just because the car is stopped doesn't mean the displacement (s) is zero.
  6. Oct 10, 2011 #5
    I don't fully understand displacement, the problems where we had to solve for displacement included a range for t, 0<= t<= 3 or something like that.
  7. Oct 10, 2011 #6


    Staff: Mentor

    According to this formula, at the moment the driver steps on the brakes (t = 0), s = 0.
    You need to find a formula for the velocity as a function of t, and determine when the velocity reaches 0.
  8. Oct 10, 2011 #7
    That function S describes the cars position as a function of time.

    You're interested in knowing when the car comes to a rest, hence you want to know how the cars velocity is changing in time.

    How can you figure out velocity if you know the cars position?
  9. Oct 10, 2011 #8
    Th velocity would be v=71-20t.
    if v=0, then 0=71-20t, so t=3.55.

    The time when the cars velocity reaches 0 is 3.55 sec.

    But if I plug t=3.55 into my origonal equation, I get s=0 ????

    Or if I set s=3.55, I get t=.0507, 3.499 ???
  10. Oct 10, 2011 #9


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Not quite, be careful with your differentiation.
  11. Oct 10, 2011 #10
    Nevermind, I see my problem.
  12. Oct 10, 2011 #11
    Thanks, v=71-40t, set equal to 0, gives me t=1.775 or 1.8.

    Thanks for all your help.
  13. Oct 10, 2011 #12


    User Avatar
    Science Advisor

    By the way, the reason the correct answer is exactly half of your answer is that with a constant acceleration, the average speed over a time interval is just the numeric average of the speed at the beginning and end of the interval.

    If the initial speed is v and the final speed is 0 (the car is stopped means the speed is 0, not the position!) the average speed is (v+ 0)/2= v/2.
  14. Oct 10, 2011 #13
    That is kinda where I was getting confused, I could get the average speed, but this question wasn't asking for that. And with my bad differentiation I was getting the wrong answers no matter which way I tried to solve it.

    Thanks for the explanation, this is an online class and there is very little explanation, I most use the Kahn Academy, You Tube, and of course the experts of PF.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook