is this correct? if not, what should i do?
how do i do this
sorry mods meant for off topic
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Smart vlr users come pt4
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Linear
First question
DISTANCE: s = 1/2a x t^2 + v0 x t
VELOCITY: s = v^2 - v0^2 / 2a
s stands for distance
part1: 0 - 9.5s
s: 1.5 x 9.5^2
s = 135.375
v: 135.375 = v^2 / 6
v: 812.25 = v^2
v = 28.5
------------------------------------
part2: 9.5s - 11.5s
s: -1.5 x 4 + 28.5 x 2
s = 51
part1 + part2 = 135.375 + 51 = 186.375m
Second question
DISTANCE: s = 1/2a x t^2 + v0 x t
VELOCITY: s = v^2 - v0^2 / 2a
GIVEN:
Sue velocity = 33.0m/s
Sue acceleration = -1.90m/s^2
Sue distance into tunnel = 0m
Van velocity = 5.20m/s
Van acceleration = 0m/s^2
Van distance into tunnel = 175m
LOOKING FOR:
distance and time
EQUATION NEEDED: (For a collision to happen, you need to have both vehicles on the same "coordinates". Thats how they collide. So in following question, we just use the basic kinematic equations and set them equal. The question asks how much time is needed. So we solve for t.
Sue_distance = Van_distance
1/2a x t^2 + v0 x t = (1/2a x t^2 + v0 x t) + 175m
-0.95 x t^2 + 33 x t = (5.2 x t) + 175
-0.95t^2 + 33t = 5.2t + 175
-0.95t^2 + 27.8t - 175 = 0
solve quadratic equation: two solutions, you pick the one closer to 0 because thats the earlier/quicker collision
t = 9.16599
Now for distance just use the same basic kinetic formula
s = 1/2a x t^2 + v0 x t
s: -0.95 x 9.16599^2 + 33 x 9.16599
s: -79.81 + 302.477
s = 222.667m
final solutions:
t = 9.16599
s = 222.667m
additional help:
https://www.mathsisfun.com/quadratic-equation-solver.html
https://www.desmos.com/calculator/ysjxt0jazm
lmk if its correct
Aye, LATEX for which I used a free of charge Overleaf cloud <-- pretty convenient and handy on the go editor.
Now also one word on the solver too... as technically you have the option to use Wolfram's API through GPT-4 by adding Wolfram as a plug-in <-- but in the paid GPT-4 version. The chat GPT part comes just as an interpreter (and pretty f-ing good one as expected) for the solver to break down the wording into algebraic form ... etc.
Regarding capabilities, both Wolfram's Mathematica and Maple were/are pretty good known calculus solvers - I remember using more Mathematica for calc but on occassions would also use Maple for linear algebra (don't recall why I specifically choose Maple over Mathematica for LinAlg though...) too back in the days before GPT. So, they have been known for their ability to get you going, beside Matlab.
Saying I'm incredibly impressed would be an understatement 🤯, as with the above combo, you could get a clear step by step explanations, and If something isn't clear, you have the option to ask for further clarification <-- this was not possible during my times, but HolyyyF... - amazing how it makes self-study so much easier, though not sure how topic of integration would be dealt, and in what details, with said method.
hehe... F-it ... you'd be more than fine with just Wolfram... you can get Maple Calc app for your phone if you need but for unlimited steps you'd need a paid subscription which depending on your budget may be okeyish ... but essentially, with khan's or/and other stuff it should be more than enough.
One more thing though, If you're into tutorial vids similar to khan, check out mathtutordvd guy <-- he's pretty good in explaining some of the complicated topics, putting them into easy to grasp scenarios etc.
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