Final answer:
To find the velocity in unit-vector notation, differentiate the position vector with respect to time. Use the given position vector and the equations for the x and y components of velocity in uniform circular motion to find the velocity in unit-vector notation.
Step-by-step explanation:
To find the velocity in unit-vector notation, we can differentiate the position vector with respect to time.
Given, r(t) = (6.00 m)i - (6.00 m)j
Diffrentiating r(t) gives, v(t) = (dx/dt)i + (dy/dt)j
Since the particle is in uniform circular motion, the x and y components of the velocity are:
dx/dt = -6.00 m * (2π/6.50 s) * sin(2πt/6.50 s)
dy/dt = 6.00 m * (2π/6.50 s) * cos(2πt/6.50 s)
Therefore, the velocity in unit-vector notation is:
v(t) = (-6.00 m * (2π/6.50 s) * sin(2πt/6.50 s))i + (6.00 m * (2π/6.50 s) * cos(2πt/6.50 s))j