Why is the answer half of my answer?


by jrjack
Tags: None
jrjack
jrjack is offline
#1
Oct10-11, 09:05 AM
P: 107
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
s=71t-20t2
0=71t-20t2
0=71-20t
t=71/20
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?
Phys.Org News Partner Science news on Phys.org
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior
Hootenanny
Hootenanny is offline
#2
Oct10-11, 09:07 AM
Emeritus
Sci Advisor
PF Gold
Hootenanny's Avatar
P: 9,789
What made you write this?
Quote Quote by jrjack View Post
0=71t-20t2
jrjack
jrjack is offline
#3
Oct10-11, 09:35 AM
P: 107
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.

Hootenanny
Hootenanny is offline
#4
Oct10-11, 09:37 AM
Emeritus
Sci Advisor
PF Gold
Hootenanny's Avatar
P: 9,789

Why is the answer half of my answer?


Quote Quote by jrjack View Post
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.
Just because the car is stopped doesn't mean the displacement (s) is zero.
jrjack
jrjack is offline
#5
Oct10-11, 09:43 AM
P: 107
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.
Mark44
Mark44 is online now
#6
Oct10-11, 09:53 AM
Mentor
P: 20,980
Quote Quote by jrjack
The position of the car is s = 71t - 20t2, t seconds after the driver applies the brakes.
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.
pergradus
pergradus is offline
#7
Oct10-11, 09:54 AM
P: 156
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?
jrjack
jrjack is offline
#8
Oct10-11, 10:02 AM
P: 107
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 ???
Hootenanny
Hootenanny is offline
#9
Oct10-11, 10:03 AM
Emeritus
Sci Advisor
PF Gold
Hootenanny's Avatar
P: 9,789
Quote Quote by jrjack View Post
Th velocity would be v=71-20t.
Not quite, be careful with your differentiation.
jrjack
jrjack is offline
#10
Oct10-11, 10:03 AM
P: 107
Nevermind, I see my problem.
jrjack
jrjack is offline
#11
Oct10-11, 10:07 AM
P: 107
Thanks, v=71-40t, set equal to 0, gives me t=1.775 or 1.8.

Thanks for all your help.
HallsofIvy
HallsofIvy is offline
#12
Oct10-11, 01:50 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879
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.
jrjack
jrjack is offline
#13
Oct10-11, 02:55 PM
P: 107
Quote Quote by HallsofIvy View Post
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.
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.


Register to reply

Related Discussions
solution stoichometry, attempted ANSWER IS WRONG, can anyone fix answer Biology, Chemistry & Other Homework 2
Statics Problem - Not sure why answer is answer Engineering, Comp Sci, & Technology Homework 5
Half-Life, Nuclear Decay Related Problem (answer in units of Ci) Introductory Physics Homework 0
Simple harmonic motion and frequency; answer disagrees from answer key Introductory Physics Homework 1
My answer 2 real answer 7 Introductory Physics Homework 6