Position

# Position - Therefore all the equations derived in the...

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Position, Velocity, and Acceleration What makes the generalization to vectors particularly simple is that the relationships between position, velocity, and acceleration stay exactly the same. Whereas before we had v(t) = x'(t) and a(t) = v'(t) = x''(t) now we have v (t) = x â≤ (t) and a (t) = v â≤ (t) = x â≤â≤ (t). where the derivatives are taken component by component. In other words, if x (t) = (x(t), y(t), z(t)) , then x â≤ (t) = (x'(t), y'(t), z'(t)) .

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Unformatted text preview: Therefore, all the equations derived in the previous section are valid once the scalar-valued functions are turned into vector-valued ones. As an example, consider the position function x (t) = a t 2 + v t + x , where a = (0, 0, - g) , v = (v x , 0, v z ) , and x = (0, 0, h) . The above vector equation for position can be broken down into three one-dimensional equations: x(t) = v x t, y(t) = 0, z(t) = - gt 2 + v z t + h...
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Position - Therefore all the equations derived in the...

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