Question

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?

Answer 1

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"`