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# pre -calc help

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A particle is moving so that its position at time t is given by the parametric equations

x = 5*sin(-2t)

y = 5*cos(2t)

What is the speed of the particle?

How do i find the speed of this particle? I'm given the parametric equations which show me the position, so would i find the slope of two given points or what?

Jan 8, 2020

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The coefficient of 5 tells us that the speed of the particle is 5.

Jan 8, 2020
#3
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These form a circle with a radius  of  5

And one complete  graph is traced out   from t = 0  to t  = pi

So.....

Speed  =   Distance Traveled   /Time      ....so....

Speed  =

2pi (5)

_____  =     10

pi

We can  also prove this with Calculus

dx/ dt  =   -10 cos (-2t)           dy/ dt   =   -10 sin (2t)

Note that  -10cos(-2t)   =  -10cos(2t)

The speed is given by

sqrt  [   (dx/dt)^2   + (dy/dt)^2  [  =

sqrt  [ (-10cos(2t))^2 +  (-10 sin (2t))^2  ]  =

sqrt  [  (-10)^2   (sin^2(2t)  + cos^2(2t)) ]   =

sqrt  (100 *  1 ] =

sqrt [ 100 ]  =

10   Jan 8, 2020