12 Two particles move along the x-axis. For 0 St 8, the position of particle P...

 

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12 Two particles move along the x-axis. For 0 St 8, the position of particle P at time t is given by xp(t) = ln(t2-2t+10), while the velocity of particle Q at time t is given by vo(t) = t2-8t + 15. Particle Q is at position x = 5 at time t = 0. a) For 0 t 8, when is particle P moving to the left? b) For 0 t8, find all times t during which the two particles travel the same direction. c) Find the acceleration of particle Q at time t = 2. Is the speed of particle Q increasing, decreasing, or neither at this time? Why? d) Find the position of particle Q the first time it changes direction. 12 Two particles move along the x-axis. For 0 St 8, the position of particle P at time t is given by xp(t) = ln(t2-2t+10), while the velocity of particle Q at time t is given by vo(t) = t2-8t + 15. Particle Q is at position x = 5 at time t = 0. a) For 0 t 8, when is particle P moving to the left? b) For 0 t8, find all times t during which the two particles travel the same direction. c) Find the acceleration of particle Q at time t = 2. Is the speed of particle Q increasing, decreasing, or neither at this time? Why? d) Find the position of particle Q the first time it changes direction.