posted by Catherine on .
A particle moves with its position given by x=cos(2t) and y=sin(t), where positions are given in feet from the origin and time t is in seconds.
A)Find the speed of the particle.
Speed = ____________
B)Find the first positive time when the particle comes to a stop.
C)If n is any odd integer, write a formula (in terms of n) for all positive times t at which the particle comes to a stop.
For the first one I got sqrt((-2sin(2t))^2+(cos(t))^2) ft/s.
I don't know ho to calculate the second and third part... please someone help...
x=cos(2t) and y=sin(t)
Speed at time t (in ft/sec)
= ... simplify as you wish
occurs when t=kπ/2, k∈Z
occurs when t=(k+1/2)π, k∈Z
So what is the smallest t when x'(t)=0 AND y'(t)=0?
Work out from B above.
Post if you more hint.