Question

An automobile travels on a straight road for 32 km at 38 km/h. It then continues in the same direction for another 32 km at 76 km/h. (a) What is the average velocity of the car during this 64 km trip? (Assume that it moves in the positive x direction.) (b) What is the average speed?

Answer 1

(a) The average velocity can be found as follows:

$$\vec{v}_{avg}=\dfrac{Displacement}{Time\ interval},$$ $$\vec{v}_{avg}=\dfrac{d_1+d_2}{\dfrac{d_1}{v_1}+\dfrac{d_2}{v_2}},$$ $$\vec{v}_{avg}=\dfrac{32\ km+32\ km}{\dfrac{32\ km}{38\ \dfrac{km}{h}}+\dfrac{32\ km}{76\ \dfrac{km}{h}}}=50.8\ \dfrac{km}{h}.$$

(b) The average speed can be found as follows:

$$v_{avg}=\dfrac{Total\ distance}{Total\ time},$$ $$v_{avg}=\dfrac{64\ km}{1.26\ h}=50.8\ \dfrac{km}{h}.$$