Define covariant and contravariant vectors. Show that velocity and acceleration are contravariant vectors.

Covariant and contravariant vectors are fundamental concepts in the study of vector spaces, particularly in differential geometry and physics.

A contravariant vector is a vector that transforms in the opposite direction of a coordinate transformation. If the coordinates of a system change, a contravariant vector will change according ___ ________ ______ __________ ________ ____ ______ _______.
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