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patbatE21
Group Title
Calculus II:
Starting at s = 0 when t = 0, an object moves along a line so that its velocity at time t is v(t) = 2t  4 centimeters per second. How long will it take to get to s = 12? To travel a total distance of 12 centimeters?
 3 years ago
 3 years ago
patbatE21 Group Title
Calculus II: Starting at s = 0 when t = 0, an object moves along a line so that its velocity at time t is v(t) = 2t  4 centimeters per second. How long will it take to get to s = 12? To travel a total distance of 12 centimeters?
 3 years ago
 3 years ago

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patbatE21 Group TitleBest ResponseYou've already chosen the best response.0
I have t=6
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
hold on, i'll compute and see if it matches
 3 years ago

patbatE21 Group TitleBest ResponseYou've already chosen the best response.0
v(t) = 2t  4 s(t) = integral 2t  4 = 2t^2  4t + C 0 = 0^2 4(0) + C t^2  4t = 12 t^2 4t 12=0 (t6)(t2) t= 6 considering time is never negative
 3 years ago

patbatE21 Group TitleBest ResponseYou've already chosen the best response.0
Grrrrrrr Idk HHHHEEEEELLLLLPPPPPP
 3 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
that will be (t6)(t+2)
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
yes i get 6 also
 3 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
second thing, u have made the displacement 0, but actually distance is needed
 3 years ago

patbatE21 Group TitleBest ResponseYou've already chosen the best response.0
he is correct
 3 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
sorry, u have made displacement 12 :)
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
yes since the velocity starts out negative, the object is going backwards at first, then goes forwards. do you want the total displacement to be 12 or the position from the starting point to be 12?
 3 years ago

patbatE21 Group TitleBest ResponseYou've already chosen the best response.0
Arnab09 would that mean I would have to integrate as suchdw:1321863723148:dw
 3 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
total distance covered, i guess
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
if you want the total displacement to be 12, then you first solve to find out where the object stopped (0 velocity) by setting v(t)=0. then plug in that t value to s(t).
 3 years ago

patbatE21 Group TitleBest ResponseYou've already chosen the best response.0
Ktklown the total distance
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
OK, so first solve to see where the object changed direction. that happened when v(t)==0, i.e. at t=2
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
at t=2 the object was at 4. then it starts going forward, so its total displacement will equal 12 when it reaches +4
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
i.e. from start (0) to 4, then from 4 back to 0 for a total of 8, then from 0 to +4 for a total of 12
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
it looks like that happens at 2+2sqrt(3) =t
 3 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
yeah,@ ktklown, u r right :)
 3 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
put the position 8 inspite of 12, u will get the answer
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
It looks like, from reading the original question, they want to know both answers. First when does it reach s=12, and second when does it travel a total of 12 (in which case we do the other computation we just finished)
 3 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
in the question, the term is 'distance', not 'displacement' so the second method is correct, definitely..
 3 years ago

patbatE21 Group TitleBest ResponseYou've already chosen the best response.0
I've worked it out 4 times today, I'm probably just bad at this
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
well it specifically says "s=12", so it seems to me like they are asking both versions. i don't know, it's not very clearly worded
 3 years ago

Arnab09 Group TitleBest ResponseYou've already chosen the best response.1
maybe, if s (displacement) =12, then t^24t=12 and t=6
 3 years ago

ktklown Group TitleBest ResponseYou've already chosen the best response.2
yeah, if i were doing this as homework i'd probably write the answer for both interpretations
 3 years ago
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