# Objects A and B are at the origin. If object A moves to #(0 ,-2 )# and object B moves to #(5 ,4 )# over #8 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

thus, if

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The relative velocity of object B from the perspective of object A can be calculated using the formula for relative velocity:

[ \text{Relative velocity} = \text{Velocity of B} - \text{Velocity of A} ]

Given that object A moves from the origin (0,0) to (0,-2) in 8 seconds, its velocity is:

[ \text{Velocity of A} = \frac{{\text{Change in position of A}}}{{\text{Time}}} = \frac{{-2 - 0}}{{8}} = -\frac{1}{4} , \text{m/s} ]

Given that object B moves from the origin (0,0) to (5,4) in 8 seconds, its velocity is:

[ \text{Velocity of B} = \frac{{\text{Change in position of B}}}{{\text{Time}}} = \frac{{5 - 0}}{{8}} = \frac{5}{8} , \text{m/s} ]

Therefore, the relative velocity of object B from the perspective of object A is:

[ \text{Relative velocity} = \text{Velocity of B} - \text{Velocity of A} = \frac{5}{8} - \left(-\frac{1}{4}\right) = \frac{5}{8} + \frac{1}{4} = \frac{7}{8} , \text{m/s} ]

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