7. The position of a car moving along a flat surface at time t is modeled by (x(t), y(t)) with velocity vector v(t) = (3+6 sin(3t), 1+ e2") for 0

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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7. The position of a car moving along a flat surface at time t is modeled by (x(t), y(t)) with velocity
vector v(t) = (3+6 sin(3t), 1+ e2") for 0 <t < 2. Both r(t) and y(t) are measured in feet, and t is
measured in seconds. At time t = 0, the car is at position (0,0).
(a) Find the position of the car at time t = 2.
(b) At what time t, for 0 <t < 2, is the line tangent to the path of the car parallel to the y-axis?
(c) Write, but do not evaluate, an integral expression that gives the total distance traveled by the
car from time t = 0 to time t = 2.
(d) Write, but do not evaluate, an integral expression that gives the average speed of the car from
time t = 0 to time t = 2.
Transcribed Image Text:7. The position of a car moving along a flat surface at time t is modeled by (x(t), y(t)) with velocity vector v(t) = (3+6 sin(3t), 1+ e2") for 0 <t < 2. Both r(t) and y(t) are measured in feet, and t is measured in seconds. At time t = 0, the car is at position (0,0). (a) Find the position of the car at time t = 2. (b) At what time t, for 0 <t < 2, is the line tangent to the path of the car parallel to the y-axis? (c) Write, but do not evaluate, an integral expression that gives the total distance traveled by the car from time t = 0 to time t = 2. (d) Write, but do not evaluate, an integral expression that gives the average speed of the car from time t = 0 to time t = 2.
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