At time tt, the position of a particle is x(t)=2sin(2t)x(t)=2sin(2t) and y(t)=3cos(2t)y(t)=3cos(2t), with 0≤t<2π0≤t<2π.
Posted: Thu Jul 14, 2022 4:37 pm
At time tt, the position of a particleis x(t)=2sin(2t)x(t)=2sin(2t) and y(t)=3cos(2t)y(t)=3cos(2t),with 0≤t<2π0≤t<2π.
(a) Below are possible graphs of the pathof the particle for 0≤t<2π0≤t<2π, indicating thedirection of motion.
(b) Find the position and velocity of theparticle when t=π/4 for:x(π4)y(π4)x′(π4)y′(π4)
(c) How many times does the particle passthrough the point found in part (b)?
(d) What does your answer topart (b) tell you about the direction ofthe motion relative to the coordinate axes when t=π4?
e) What is the speed of the particle attime t=π?
(a) Below are possible graphs of the pathof the particle for 0≤t<2π0≤t<2π, indicating thedirection of motion.
(b) Find the position and velocity of theparticle when t=π/4 for:x(π4)y(π4)x′(π4)y′(π4)
(c) How many times does the particle passthrough the point found in part (b)?
(d) What does your answer topart (b) tell you about the direction ofthe motion relative to the coordinate axes when t=π4?
e) What is the speed of the particle attime t=π?