An object travels North at # 8 m/s# for #3 s# and then travels South at # 7 m/s# for # 8 s#. What are the object's average speed and velocity?

1 Answer
Apr 26, 2018

Answer:

Average Speed

#bar(v)~~7.27color(white)(l)"m"*"s"^(-1)#

Average Velocity

#bar(sf(v))~~5.54color(white)(l)"m"*"s"^(-1)#

Explanation:

#"Speed"# equals distance over time whereas
#"Velocity"# equals displacement over time.

Total distance travelled- which is independent of the direction of motion- in #3+8=11color(white)(l)"seconds"#

#Delta s=s_1+s_2=v_1*t_1+v_2*t_2=8*3+7*8=80color(white)(l)"m"#

Average speed

#bar(v)=(Delta s)/(Delta t)=(80color(white)(l)"m")/(11color(white)(l)"s")~~7.27color(white)(l)"m"*"s"^(-1)#

The two components of the final displacement, #sf(x)_1# and #sf(x)_2#, are normal (a.k.a., perpendicular ) to each other.

Hence, directly apply the Pythagorean theorem to find the
displacement from the initial position after #11color(white)(l)"seconds"#

#Delta sf(x)=sqrt(sf(x)_1^2+sf(x)_2^2)=sqrt((sf(v)_1*t_1)^2+(sf(v)_2*t_2)^2)#

#=sqrt((8*3)^2+(7*8)^2)=8sqrt(58)color(white)(l)"m"#

Average velocity

#bar(sf(v))=(Delta sf(x))/(Delta t)=(8sqrt(58)color(white)(l)"m")/(11color(white)(l)"s")~~5.54color(white)(l)"m"*"s"^(-1)#