6. Particle P moves along the x-axis such that, for time t > 0, its position is given by xp(t) =

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6. Particle P moves along the x-axis such that, for time $t > 0$, its position is given by $x_p(t) = 6 - 4e^{-t}$. Particle Q moves along the y-axis such that, for time $t > 0$, its velocity is given by $v_Q(t) = frac{1}{t^2}$. At time $t = 1$, the position of particle Q is $y_Q(1) = 2$. (a) Find $v_p(t)$, the velocity of particle P at time t. (b) Find $a_Q(t)$, the acceleration of particle Q at time t. Find all times t, for $t > 0$, when the speed of particle Q is decreasing. Justify your answer. (c) Find $y_Q(t)$, the position of particle Q at time t. (d) As $t o infty$, which particle will eventually be farther from the origin? Give a reason for your answer.

          6. Particle P moves along the x-axis such that, for time $t > 0$, its position is given by $x_p(t) = 6 - 4e^{-t}$.
Particle Q moves along the y-axis such that, for time $t > 0$, its velocity is given by $v_Q(t) = frac{1}{t^2}$. At time $t = 1$,
the position of particle Q is $y_Q(1) = 2$.
(a) Find $v_p(t)$, the velocity of particle P at time t.
(b) Find $a_Q(t)$, the acceleration of particle Q at time t. Find all times t, for $t > 0$, when the speed of
particle Q is decreasing. Justify your answer.
(c) Find $y_Q(t)$, the position of particle Q at time t.
(d) As $t 	o infty$, which particle will eventually be farther from the origin? Give a reason for your answer.

$6. Particle P moves along the x-axis such that, for time t > 0, its position is given by xp(t) = 6 - 4e^-t. Particle Q moves along the y-axis such that, for time t > 0, its velocity is given by vQ(t) = frac1t^2. At time t = 1, the position of particle Q is yQ(1) = 2. (a) Find vp(t), the velocity of particle P at time t. (b) Find aQ(t), the acceleration of particle Q at time t. Find all times t, for t > 0, when the speed of particle Q is decreasing. Justify your answer. (c) Find yQ(t), the position of particle Q at time t. (d) As t o infty, which particle will eventually be farther from the origin? Give a reason for your answer.$

Added by Adriana J.

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