velocity is contravariant tensor becasue displacement tensor is contravariant.

"Derivative of"

well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.

Velocity is the derivative of position.

Velocity is the derivative of position.

Velocity is the derivative of position.

Velocity is the derivative of position.

A dot A = A2

do a derivative of both sides

derivative (A) dot A + A dot derivative(A) =0

2(derivative (A) dot A)=0

(derivative (A) dot A)=0

A * derivative (A) * cos (theta) =0

=> theta =90

A and derivative (A) are perpendicular