An object travels North at #6 m/s# for #2 s# and then travels South at #6 m/s# for #7 s#. What are the object's average speed and velocity?

1 Answer
May 25, 2018

Answer:

Refer to the explanation.

Explanation:

Average speed is defined through the equation:

#bars=d/t#

where:

  • #bars# is the average speed

  • #d# is the total distance covered

  • #t# is the time taken

So, we get:

#bars=(6 \ "m/s"*2 \ "s"+6 \ "m/s"+7 \ "s")/(9 \ "s")#

#=(54 \ "m")/(9 \ "s")#

#=6 \ "m/s"#

Velocity is given by the equation:

#barv=(vecd)/t#

where:

  • #barv# is the average velocity

  • #vecd# is the distance covered in a specific direction

  • #t# is the time taken

Here, I'll let the standard direction to be north. So, the south direction will be represented as negative.

So, we get:

#barv=(6 \ "m/s"*2 \ "m/s"-6 \ "m/s"*7 \ "s")/(9 \ "s")#

#=(-30 \ "m")/(9 \ "s")#

#=-3.bar(3) \ "m/s"#

Therefore, the average velocity is #3.33 \ "m/s"# south.