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?
These form a circle with a radius of 5
And one complete graph is traced out from t = 0 to t = pi
Speed = Distance Traveled /Time ....so....
_____ = 10
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 ] =