The instantaneous position of an object is specified by its position vector leading from a fixed origin to the location of the object modeled as a particle. suppose for a certain object the position vector is a function of time, given by r with arrow = 3 î + 2 ĵ − 3t k, where r with arrow is in meters and t is in seconds. (a) evaluate dr with arrow/dt. ( î + ĵ + k) m/s (b) what physical quantity does dr with arrow/dt represent about the object?

(a)

(b) Instantaneous velocity of the object is represented by .

Explanation:

Given:

        where is in meters and is in seconds.

Part (a):

Part (b):

As we know that the rate of change of position is the velocity of a particle which is calculated by the differential of the position vector of the particle at with respect to time. This differential gives us a unit vector along negative z-axis having unit as m/s. So, the physical quantity represented by is the instantaneous velocity of the object.

explanation:

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the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it