Calculus (urgent!!)
posted by Catherine .
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...

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.
Respond to this Question
Similar Questions

calculus
a particle moves along a number line measured in cm so that its position at time t sec is given by s=72/(t+2) +k, k is a constant and t>=0 seconds. (a) Find the instantaneous velocity of the particle at t=4 seconds (b) Find the … 
Calculus (urgent!!)
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 … 
calculus
5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5? 
calculus
A particle moves on the xaxis so that its velocity at any time t is given by v(t) = sin 2t. At t = 0, the particle is at the origin. a)For 0 ≤ t ≤ π, find all values of t for which the particle is moving to the left. … 
Physics
A particle moves in a straight line so that its position (x cm) from a fixed point O at time (t seconds) is given by x= t^36t^215t5 Find the average speed of the particle in the first 7 seconds 
Calculus
The position of a particle moving on a horizontal line is given by s(t)=2t^315t^2+24t5, where s is measured in feet and t in seconds. a: What is the initial position of the particle? 
AP CALC. AB
1.The position of a particle moving on the line y = 2 is given by x(t)= 2t^313t^2+22t5 where t is time in seconds. When is the particle at rest? 
calculus
A particle moves so that its position is given by ⟨cos(t),sin(t),cos(6t)⟩. Find the maximum and minimum speeds of the particle. 
Calculus
A particle moves along the xaxis so that at any time t, measured in seconds, its position is given by s(t) = 5cos(t) − sin(3t), measured in feet. What is the acceleration of the particle at time t = π seconds? 
Calculus
The Question: A particle moves along the Xaxis so that at time t > or equal to 0 its position is given by x(t) = cos(√t). What is the velocity of the particle at the first instance the particle is at the origin?