The velocity is the derivative of position.
... v(t) = r'(t) = -5sin(t)i +4cos(t)j . . . . velocity
The acceleration is the derivative of velocity.
... a(t) = v'(t) = -5cos(t)i -4sin(t)j . . . . acceleration
The speed is the magnitude of velocity.
... s(t) = ||v(t|| = √((-5sin(t))² +(4cos(t))²)
... = √(25sin(t)² +16(1 -sin(t)²))
... s(t) = √(16 +9sin(t)²) . . . . speed
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Of course, derivatives of these functions are found from ...
... (d/dt)(sin(t)) = cos(t); (d/dt)(cos(t)) = -sin(t); (d/dt)(a + b) = da/dt + db/dt.
