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.