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 3 years ago
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
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?

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

patbatE21
 3 years ago
Best ResponseYou've already chosen the best response.0v(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

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

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

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

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

ktklown
 3 years ago
Best ResponseYou've already chosen the best response.2yes 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?

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

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

ktklown
 3 years ago
Best ResponseYou've already chosen the best response.2if 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).

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

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

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

ktklown
 3 years ago
Best ResponseYou've already chosen the best response.2i.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

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

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

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

ktklown
 3 years ago
Best ResponseYou've already chosen the best response.2It 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)

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

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

ktklown
 3 years ago
Best ResponseYou've already chosen the best response.2well 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

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

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