Question

An object travels North at `6 m/s` for `4 s` and then travels South at `3 m/s` for `5 s`. What are the object's average speed and velocity?

Answer 1

`"Speed" = (4.3333333333bar3m)/s`

`"Velocity" = (1m)/s`

Explanation:

Calculating the average speed is very easy but I'm first doing average velocity because it requires more attention

`color(white)(xxxxxxxxxxxx)O`
`N larr larr larr larr A rarr rarr rarr rarr S`

Where A is the point where the object started from
N is north and S is south and is considered the midway between north andsouth. In our real earth that's equator
O is the object

The main trick here is to measure the distance between A and the point where the car stops.

Distance covered towards North

`(6m)/s xx 4 = 24m`

It is 24meters ahead of A towards north direction

It can be represented like this
`color (white)(xxxxxxxx )24m`
`color(white)(xxxxx )Ocolor(white)(xx )harr`
`N larr larr larr larr A rarr rarr rarr rarr S`

Distance between A and O = 24m

Now calculate the distance moved towards South

`(3m)/s xx 5 = 15m`

`color(white)(xxxxx )Orarr"by 15 meters"`
`N larr larr larr larr A rarr rarr rarr rarr S`

Distance moved from A

= 24m -15m = 9m

Time elapsed

4s + 5s = 9s

= 9m/9s = 1m/s is the velocity

`"Speed" = "distance"/"time"`

Distance is the distance covered can be anywhere in any direction in any zigzag pattern means the object can move back and front , eft and right.

So distance covered = 24m + 15m = 39m

Time elapsed

4s + 5s = 9s

= `"distance"/"time" = (39m)/(9s) = (4.3333333333bar3m)/s`