A particle moves along the x-axis so that its velocity at time t is given by the function whose graph is shown below. At which time is the particle furthest from the origin?

Question

anonymous · Answer

(A) t=.5
(B) t=1.5
(C) t=2
(D) t=2.8
(E) t=3

anonymous · Answer

so you know that the distance is the area underneath the curve, so you gotta look at which point is the area the greatest. keep in mind that area can be either positive or negative, so you want the point that will give you the greatest positive area because the greater the area, then the greater the distance that you will be from the origin. [:

anonymous · Answer

Ok, so the greatest distance from the origin = greatest positive area, which would be @ t=2 - correct?

anonymous · Answer

ermm not quite. you have to account for alll of the positive area! when youre looking at area dont worry about whether the slope is positive or negative, but whether the area itself is in the top quadrant or the bottom quadrant.

anonymous · Answer

@shuchii then how would this be at one specific x (in this case, t) value?

anonymous · Answer

well for this case it would be at t=2.8 because when velocity is zero and then heads negative, thats the time when the particle heads in the opposite direction. does that make sense? so the spot at which you stop before you go in the opposite direction technically gives you the greatest area, and thus distance, yeah? [:

anonymous · Answer

Yes, I can visualize it now! And that's why it's important for it to be the greatest POSITIVE area. Thank you very much.

anonymous · Answer

no problem [: let me know if you need more help with these types of problems [: