+0  
 
0
54
3
avatar

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
 #1
avatar
0

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

 Jan 8, 2020
 #2
avatar
0

 Jan 8, 2020
 #3
avatar+107107 
+1

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

 

 

 

 

cool cool cool

 Jan 8, 2020

34 Online Users

avatar