Gina V.

# looking for help with derivatives

Particle P moves along the x-axis so that its position at time t>0 is given by xP(t)= (e^(2−t)−2t) / (e^(2−t)+3t). A second particle, particle Q , also moves along the x -axis so that its position at time t is given by xQ(t)=t^3−3t^2+5 .

a) Show that the velocity of particle P at time t is given by vP(t)= −5te^(2−t)−5e^(2−t) / (e^(2−t)+3t)^2 .

b) At time t=2 , particle Q is at rest. At time t=2 , is particle P moving toward particle Q or away from particle Q ? Explain your reasoning.

c) The acceleration of particle Q is given by aQ(t) . Find the value of aQ(2) .

d) Describe the position of particle P and the position of particle Q as t approaches infinity. How did you get to your answers.