Gigi N.

asked • 04/12/21

I need some help with math

For 0 ≤ t ≤ 12 , a roller coaster car has position (x(t),y(t)) with velocity vector ⟨10, −tsin(πt/4)⟩ , where x(t) and y(t) are measured in meters and t is measured in seconds. At time t=0 , the car is at position (0,18) .

a) What is the slope of the line tangent to the path of the car at time t=2?

b) What is the speed of the car at time t=6 ?

c) During the time interval 0 ≤ t ≤ 12 , what is the maximum value of y(t)?

d) Write, but do not evaluate, an expression that gives the average speed of the car over the time interval 0 ≤ t ≤ 12.

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