The postion of a particle is defined by r={5cos(2t)i+4sin(2t)j}m, where t is in seconds and the arguments for sine and cosine are give in radians. Determine magnitudes of velocity and acceleration of the particle when t=1s. Also, prove that the path of the particle is elliptical.

work so far:
v=5cos(2t)d/dt i + 4sin(2t)d/dt j =-10sin(2t)i+8cos(2t)j
magnitude of v @t=1 is √((10sin(2))2+(8cos(2))2)=9.68m/s a=-10sin(2t)d/dt i +8cos(2t)d/dt j=-20cos(2t)i-16sin(2t)j
magnitude of a @t=1 is √((20cos(2))2+(16sin(2))2)=16.76m2/ s
now for the part i'm stuck
standard form of an ellipse is (x-h)2/a2+(y-k)2/b2=1
let h and k =0 then you have x2/a2+y2/b2=1
not even sure where to start to prove that this is equal to 5cos(2t)i+4sin(2t)j

the clapeyron equation (also called the clausius-clapeyron equation) relates the slope of a reaction line on a phase diagram to fundamental thermodynamic properties.

explanation:

answer:

the fed will purchase bonds from banks to inject money into the banking system. the banks can use these funds to provide loans to individuals and businesses.

explanation:

key points:

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