Net Change Theorem & Particle Motion
Unit 6 Class #9
#3:
(hours) 0
Vp(t ) I
(meters per hour) 0
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The velocity of a particle P, moving along the x-axis is given by the differentiable function vp, where vp(t) is
measured in meters per hour and tis measured in hours. Selected values of vp(t) are shown in the table above.
Particle Pis at the origin at time t = 0.
(a) Justify why there must be at least one time t, for 0.3 :5 t :5 2.8 at which v;(t), the acceleration of particle P,
equals 0 meters per hour per hour.
(b) Using a trapezoidal sum with the three subintervals [0,0.3], [0.3,1.7], and [1.7,2.8] to approximate the value of
fo2 .s vp(t) dt.
(c) A second particle Q, also moves along the x -axis so that its velocity for 0 :5 t :5 4 is given by
vQ(t) = 45../t cos(0.063t2) meters per hour. Find the time interval during which the velocity of particle Q is at
least 60 meters per hour. Find the distance traveled by particle Q during the interval when the velocity of particle Q
is atleast 60 meters per hour.
(d) At time t = 0, particle Q is at position x = -90. Using the result from part (b) and the function vQ from part (c),
approximate the distance between particles P and Q at time t = 2.8.