Posted by **Catherine** on Friday, April 15, 2011 at 1:10am.

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 = ____________

(include units)

B)Find the first positive time when the particle comes to a stop.

t=_____

(include units)

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.

t=______

(include units)

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...

- Calculus (urgent!!) -
**MathMate**, Friday, April 15, 2011 at 10:31am
x=cos(2t) and y=sin(t)

x'(t)=-2sin(2t),

y'(t)=cos(t)

A.

Speed at time t (in ft/sec)

= sqrt(x'(t)²+y'(t)²)

= sqrt(4sin²(2t)+cos²(t))

= ... simplify as you wish

B.

x'(t)=-2sin(2t)=0

occurs when t=kπ/2, k∈Z

and y'(t)=cos(t)=0

occurs when t=(k+1/2)π, k∈Z

So what is the smallest t when x'(t)=0 AND y'(t)=0?

C.

Work out from B above.

Post if you more hint.

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