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A particle, P, is moving along the X-axis. The velocity of particle P at time t is given by Vp(t) = sin(5t) for 0 â‰¤ t â‰¤ %. At time t = 0, particle P is at position x = 5. A second particle, Q, also moves along the X-axis. The velocity of particle Q at time t is given by Vq(t) = 1.8t – 1.25 for 0 â‰¤ t â‰¤ #. At time t = 0, particle Q is at position x = 10.

(a) Find the positions of particles P and Q at time t.

(b) Are particles P and Q moving toward each other or away from each other at time t = ? Explain your reasoning.

(c) Find the acceleration of particle Q at time t. Is the speed of particle Q increasing or decreasing at time t? Explain your reasoning.

(d) Find the total distance traveled by particle P over the time interval 0 â‰¤ t â‰¤ T.

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01:57

A particle, P; is moving along the x-axis. The velocity of particle P at time is given by Vp(t) sin(,”5) for 0 <n<t At time t = 0. particle P is at position x = 5.A second particle, Q, also moves along the x-axis. The velocity of partiele at time t is given by ve(t) (t _ 1.8) 1.25′ for 0 < t < t. At time t = 0_ particle Q is at position x = 10.Find the positions of particles P and Q at time t = [.(b) Are particles P and Q moving toward each other or away from each other at time =[ ? Explain your reasoning:Find the acceleration of particle Q at time =IIs the speed of particle Q increasing or decreasing at time t = [ Explain your reasoning:Find the total distance traveled by particle P over the time interval 0 < t < T_

02:09

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 vO(t).

At time t = 1, the position of particle Q is yO(1) = 2.

(a) Find vP(t), the velocity of particle P at time t.(b) Find aO(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 yO(t), the position of particle Q at time t.(d) As t approaches infinity, which particle will eventually be farther from the origin? Give a reason for your answer.

06:41

Two particles move along the x-axis. For 0 < t < 6, the position of particle P at time given by p(t) = 4cos(t), while the position of particle R at time is given by r(t) = t^3 – 6t^2 + 9t + 3.For 0 < t < 6, find all times during which the particle R is moving to the left. Justify your answer.Find the total distance traveled by the particle R over the time interval 0 < t < 4. Fully justify your answer.For 0 < t < 6, find all times during which the particles travel in opposite directions.Find the acceleration of particle P at time t, whether it is slowing down or doing neither.Is the particle P speeding up? Explain your reasoning.

03:52

A particle moves along the x-axis so that its velocity at time 0 is less than or equal to t is less than or equal to 5 is given by v(t) = sin(t) + 2cos(t). The position of the particle at time t is x(t) and x(0) = 1. A) Find the acceleration of the particle at time t = 3. B) Find the total distance traveled by the particle from time t = 0 to t = 3. C) Find the position of the particle at time t = 3.

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