Answer to Question #161790 in Mechanics | Relativity for Dr. Horus

Question

What is the average velocity of a man who ran a distance of 3km at a

velocity of 7.5 m/s, and the walked 1km at a velocity of 0.8 m/s?

Answer 1

Average velocity can be found as follows:

$$v_{avg}=\dfrac{Total\ displacement}{Total\ time\ taken}=\dfrac{d_{tot}}{t_{tot}}.$$

Let's find the total displacement:

$$d_{tot}=d_1+d_2=3000\ m+1000\ m=4000\ m.$$

Let's find the total time taken:

$$t_{tot}=\dfrac{d_1}{v_1}+\dfrac{d_2}{v_2},$$ $$t_{tot}=\dfrac{3000\ m}{7.5\ \dfrac{m}{s}}+\dfrac{1000\ m}{0.8\ \dfrac{m}{s}}=1650\ s.$$

Finally, we can find the average velocity:

$$v_{avg}=\dfrac{4000\ m}{1650\ s}=2.42\ \dfrac{m}{s}.$$