An object travels North at #15 m/s# for #2 s# and then travels South at #2 m/s# for #8 s#. What are the object's average speed and velocity?

1 Answer
Sep 7, 2017

Answer:

speed = 4.6 m/s
velocity = 1.4 m/s (north) or -1,4m/s (south)

Explanation:

To start of, we have to find the the total distance (or disposition covered) north and south which can be derived from the speed (or velocity) formula and total time taken
#speed="distance"/"time"#

therefore,
#"distance"=speed*time#

When the object is traveling north:
#"distance"=15*2=30 meters#

When the object is traveling south
#"distance"=2*8=16 meters#

#Total time = 2+ 8=10 seconds#

Now we have to distinguish between speed and velocity, since they are similar but they are not the same thing.

Speed is #"total distance covered" / "time"#

however,

Velocity is #"total disposition"/"time"#

Distance is not the same as disposition, as distance is a scalar quantity while disposition is a vector quantity.

Scalar quantities do not have direction, so the calculations are done without calculation,

#"distance"= 30 meters + 16 meters = 46 meters#
thus
#"speed"=46/10=4.6 "m/s"#

But, vector quantities are affected by direction, so we have to check the directions in calculations,

#"disposition"= 30 "meters (north)" -16 "meters (south)" = 14 "meters (north)" # (the minus sign is because north is opposite direction to south)
thus,
#"velocity"=14/10=1.4 "m/s" (north)#

when calculated to south, the velocity will be #16-30=-14 "m/s south"#