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a particle moves along the x-axis with the velocity v(t)=cos(1/2t) for time t_>0. if the particle is at the position x=2 at time t=3pi, determine if the particle is moving towards the origin or away from the origin at time t=7pi/3



Answer :

Nytex

Answer:

7pi/3

Step-by-step explanation:

To find out if the particle is moving towards or away from the origin at time t = 7pi/3, we look at the velocity function v(t) = cos(1/2 * t).

When we plug in t = 7pi/3 into the velocity function, we get:

v(7pi/3) = cos(1/2 * 7pi/3) = cos(7pi/6)

The cosine of 7pi/6 is a negative number because 7pi/6 is an angle that falls in the third quadrant of the unit circle, where cosine values are negative.

Since the velocity is negative at t = 7pi/3, this means the particle is moving in the negative direction on the x-axis. Therefore, the particle is moving towards the origin at t = 7pi/3.

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