15. A car traveling at 50 m/s applies its brakes. The brakes slow the car at a rate of 3m/s2. If the car slows to a speed of 26 m/s, how far did it travel while the brakes were being applied?

Question

amistre64 · Answer

what physics formulas are you aware of for this?

goformit100 · Answer

Welcome to Open Study .................. Sir/Ma'am @habibmiranda

amistre64 · Answer

otherwise we can develop one using calculus

anonymous · Answer

Well, I know the basic x=.5at^2 and v=sqrt(2ax)

anonymous · Answer

I have not yet taken a calculus class... :(

amistre64 · Answer

those are fine

the  x=.5at^2  will do fine, but needs to be modified at least in my mind.

anonymous · Answer

Ok. how so?

amistre64 · Answer

a is causing the car to slow down, so do you agree that its going to be negative?  and at a rate of 3?

anonymous · Answer

yea, I figured that.

amistre64 · Answer

x=-3(.5) at^2

but we have a starting velocity,  we start at 50t

 x = -3(.5) at^2 + 50t

now, at t=0 we have a place to start

to find the speed at any moment,  i have to resort to calculus since its what i know best and can never recall the formulas lol

v = -3(2)(.5)t + 50,  for what value of t does v = 26?

amistre64 · Answer

$$v-vi=at$$ might be the formula?

amistre64 · Answer

v_i  that is

amistre64 · Answer

starting to recall my physics class lol.
$$v_f-v_i=at$$$$26-50=-3t$$
there for$$x=-\frac{3}{2}t^2$$
suffices for distance traveled.

anonymous · Answer

I guess I'm a little lost on how to find t.

amistre64 · Answer

um ... divide by -3 of course.

amistre64 · Answer

$$v_f=at+v_i$$
$$v_f-v_i=at$$
$$\frac{v_f-v_i}{a}=t$$
if we simply wnat to sub this in then:
$$x=\frac{a}{2}\left(\frac{v_f-v_i}{a}\right)^2$$

anonymous · Answer

that gives me a value of -8 for time and when I plug it in to find x it gives me 96 meters
 which is the wrong answer. The answer is supposed to be 304 meters

amistre64 · Answer

26 - 50 = -24

-24/-3 = 8 ... but then 8^2 = -8^2  so that shouldnt be an issue

x = .5(-3) * 8^2

x = -3(32) = 96

let me try it my calculus way ..... see if i get the same results.

anonymous · Answer

ok. sounds good. I appreciate all your help BTW.

amistre64 · Answer

a = -3;  integrate to get velocity
...............................................

v = -3t + C  such that v(0) = 50;  C = 50

v = -3t + 50; integrate to get position

when v=26,  t=8
.................................................

s = -3/2 t^2 + 50t + K  such that at s(0) we have a starting position of 0 to measure from.  K = 0


s = -3/2 t^2 + 50t  gives us our position

when t=8 we get .... 304

anonymous · Answer

So would you say that in order to solve this problem we need to know calculus?

amistre64 · Answer

need to know calculus?  no.  you just have to remember the proper formulas that the physics book give us ....

amistre64 · Answer

i just work better from a calculus point of view :)  since i cant remember a formula for the life of me lol

anonymous · Answer

I guess that's my problem. I don't recall what formula that would solve this from my book. Was it a derivation of a more common equation?

amistre64 · Answer

one way to consider it is:

a = -3

v = -3t;  v = 50 when t=-50/3
             v = 26 when t = -26/3

the position of x when t = -50/3 is:  a
the position of x when t = -26/3 is:  b

the difference between a and b is the distance traveled.

anonymous · Answer

Ok. That's actually very helpful.

amistre64 · Answer

its an approach for using the stuff that we can recall :)

anonymous · Answer

Thanks again. You were awesome!

amistre64 · Answer

youre welcome, and good luck :)