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anonymous
 one year ago
A particle moves along the xaxis with velocity v(t) = t^2 − 4, with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = 3 seconds.
anonymous
 one year ago
A particle moves along the xaxis with velocity v(t) = t^2 − 4, with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = 3 seconds.

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Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1For the distance you need to know the positive and negative values because if you integrate from 0 to 3 you just have the displacement.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so how would you find those

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Well we know v(t) = t^24 =(t+2)(t2), notice this gives us the negative value when v(t) is going in the opposite directions, so you will have to take absolute values of when it goes from \[\left \int\limits_{0}^{2} t^24 dt\right + \left \int\limits_{2}^{3} t^24dt \right\] notice that distance is just \[\int\limits_{0}^{3} v(t) dt\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1From 0<t<2 it's negative and 2<t<3 it's positive so we take the absolute value for that reason

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the answer would be 3.0333?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1No, remember we are taking the absolute value

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1That makes negative = +

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yes so it would be 7.6

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1distance can't be negative, it's a scalar value

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that looks good \[\frac{ 23 }{ 2 } \approx 7.7\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1So it worked out?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes it did and it made a lot of sense the way you explained it thank you
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