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.

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