Video: Determining the Magnitude of the Displacement Vector Based on Time and the Expression of the Position Vector

A particle moving in a straight line has a position vector 𝐫, defined by the relation 𝐫 = (𝑑² + 3)𝐧, where 𝑑 is the time measured in seconds and 𝐧 is a unit vector. Determine the magnitude of the displacement vector 𝐬 in meters after 4 seconds

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Video Transcript

A particle moving in a straight line has a position vector 𝐫 defined by the relation 𝐫 is equal to 𝑑 squared plus three 𝐧, where 𝑑 is the time measured in seconds and 𝐧 is a unit vector. Determine the magnitude of the displacement vector 𝐬 in meters after four seconds.

Displacement is the change in position of an object. The displacement after four seconds will be the position in relation to the position at the start. We can therefore say that the displacement after four seconds is 𝐫 of four minus 𝐫 of zero. Substituting 𝑑 is equal to four gives us four squared plus three 𝐧. And substituting 𝑑 is equal to zero gives us zero squared plus three 𝐧. As four squared is equal to 16, we have 19𝐧 minus three 𝐧. The vector 𝐬 after four seconds is therefore 16𝐧. As 𝐧 is the unit vector and our units are meters, the magnitude of the displacement vector after four seconds is 16 meters.

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