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The velocity function of a moving particle on a coordinate line is v(t) = 3cos(2t) for...

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veteran25 | Student | Honors

Posted October 27, 2012 at 3:19 PM via web

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The velocity function of a moving particle on a coordinate line is v(t) = 3cos(2t) for 0 is less than or equal to t

 

and 2pi is greater than or equal to t

(a) Determine when the particle is moving to the right.

Tagged with calculus 2, math

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted October 28, 2012 at 5:22 PM (Answer #1)

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Obviously particle will move to the right when velocity is >0. cos x>0 implys that x is in 1st or 4th quadrant. So for your function that is for 0+k*2pi<=2t<pi/2+k*2pi and

3pi/2+k*2pi<2t<=2pi+k*2pi, 

where k is integer.

Deviding first inequality by 2 you get

0 + k*pi<=t<pi/4 + k*pi 

and  deviding second inequality by 2 you get 

3pi/4 + k*pi <t<=pi + k*pi 

So for k=0 and k=1 you get your solution.

Particle is moving ot the right when 

t is from [0,pi/4] U [3pi/4,5pi/4] U [7pi/4,2pi].

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