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

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)