The displacement of a point over a time interval t 1 to t 2 is defined to be the

Question

The displacement of a point over a time interval t1 to t2 is defined to be the difference of the position vectors-that is, r(t2)-r(t1). For the following, find the displacement and the magnitude of the displacement over the interval t=4s to t=6s. Note that i,j,k are mutually perpendicular unit vectors having directions fixed int he frame of reference. vp is the velocity of a point P moving in the frame.

1.

2.

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Explanation / Answer

Integrating Vp gives us the position vector. 1. r(t) = 6t2i - 36/t j - t3k So, r(6) - r(4) = 120i + 3j -152k-->displacement Magnitude = v(1202+9+1522) = 2. r(t) = -80/p cos(pt/4) i - 80/p sin(pt/4) => r(6)-r(4) = 80/p j - 80/p i magnitude = 36 m 3. r(t) = -50e-0.1ti + 10e-0.4tj => r(6)-r(4) = -6.075i -1.1j magnitude = v6.0752+1.12 = 6.17 m

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