A car makes a trip due west for three-fourths of the time anddue east one-fourth

Question

A car makes a trip due west for three-fourths of the time anddue east one-fourth of the time. The average westward velocity hasa magnitude of 25 m/s, and the average eastward velocity has amagnitude of 17 m/s. What is the average velocity, magnitude anddirection, for the entire trip?
This is how I've set it up: Average velocity west: = -25 m/s = (-18.75 m) / (3/4 s) Average velocity east: = 17 m/s = (4.25 m) / (1/4 s) A car makes a trip due west for three-fourths of the time anddue east one-fourth of the time. The average westward velocity hasa magnitude of 25 m/s, and the average eastward velocity has amagnitude of 17 m/s. What is the average velocity, magnitude anddirection, for the entire trip?
This is how I've set it up: Average velocity west: = -25 m/s = (-18.75 m) / (3/4 s) Average velocity east: = 17 m/s = (4.25 m) / (1/4 s)

Explanation / Answer

Let the east direction be positive and west direction benegative.SInce east and west are opposite to each other then velocity ineast direction v = 17 m / s velocity in west direction v ' = -25 m / s Total time for a trip = t then distance travel in east direction S = v * ( 1/ 4 t)   Since in east direction it travel 1/4 th of thetme                                                           = 17 t / 4                                                           = 4.25 t distance travel in west direction S ' = v ' *( 3/ 4 t )   Since in west direction it travel 3/4 th ofthe tme                                                           = 3v' t / 4                                                           = -18.75 t total displacement S " = S + S '                                  = 4.25 t -18.75 t                                  = -14.5 t Therefore average velocity   V = S " / t                                               = -14.5 i.e., itis in west direction                                                           = 3v' t / 4                                                           = -18.75 t total displacement S " = S + S '                                  = 4.25 t -18.75 t                                  = -14.5 t Therefore average velocity   V = S " / t                                               = -14.5 i.e., itis in west direction

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