The location of a particle (in m) is given by its x, y and z coordinates as func

Question

The location of a particle (in m) is given by its x, y and z coordinates as function of the time (in seconds)? The location of a particle (in m) is given by its x, y and z coordinates as function of the time (in seconds) as:
x = -73+17t+13t2 and y = -9-25t and z = -67-7t-9t2

Calculate the magnitude of the displacement from t = 3.00 s to t = 12.00 s.
calculate the y-component of the average velocity between t = 3.00 s and t = 12.00 s? The location of a particle (in m) is given by its x, y and z coordinates as function of the time (in seconds)? The location of a particle (in m) is given by its x, y and z coordinates as function of the time (in seconds) as:
x = -73+17t+13t2 and y = -9-25t and z = -67-7t-9t2

Calculate the magnitude of the displacement from t = 3.00 s to t = 12.00 s.
calculate the y-component of the average velocity between t = 3.00 s and t = 12.00 s?

Explanation / Answer

P(t) = (-73+17t+13t^2)i + (-9-25t)j + (-67-7t-9t^2)k

P(3) = 95 i -84 j -169 k

P(12) = 2003 i -309 j - 1447 k

displacement = (2003 - 95)i + (-309 +84)j + (-1447 +169)k = 1908 i + -225j -1278k

magnitude = 2307.46 m

y-component of the average velocity = (-309 +84)/(12- 3) = -25 m/s

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