Unformatted text preview: will be another vector. The resulting vector will be directed tangential to the curve that represents the function. • Scalar Differentiation in different coordinate systems . An important scalar variable used in differentiations is the time t . Based on the position vector, we can obtain the velocity and acceleration vectors by differentiating the position vectors once and twice, respectively, with respect to time. If the Cartesian coordinates are being used, the axes are independent of time, and differentiation the position vector with respect to time is equivalent to differentiating the individual components with respect to time: v = r = dx i dt ˆ x i i ∑...
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 Spring '09
 MORGAN
 Physics, Vector Space, Coordinate system, scalar diﬀerentiation

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