Answer to Question #168615 in Physics for Phyroe

Question

An auto travels at the rate of 25km/h for 4.0 minutes, then at the 50 km/h at 8.0 minutes and finally at 20 km/h at 2.0 minutes. Find (a) the total distance covered in km and (b) the average speed for the complete trip in m/s.

Answer 1

(a) Let's first find the total distance traveled:

$$d_{tot}=d_1+d_2+d_3,$$ $$d_{tot}=v_1t_1+v_2t_2+v_3t_3,$$

$d_{tot}=25\ \dfrac{km}{h}\cdot(4\ min\cdot \dfrac{1\ h}{60\ min})+50\ \dfrac{km}{h}\cdot(8\ min\cdot \dfrac{1\ h}{60\ min})+20\ \dfrac{km}{h}\cdot(2\ min\cdot \dfrac{1\ h}{60\ min})=9\ km.$

(b) We can find the average speed for the complete trip as follows:

$$v_{avg}=\dfrac{d_{tot}}{t_{tot}},$$ $$v_{avg}=\dfrac{9\ km}{4\ min\cdot \dfrac{1\ h}{60\ min}+8\ min\cdot \dfrac{1\ h}{60\ min}+2\ min\cdot \dfrac{1\ h}{60\ min}},$$ $$v_{avg}=38.57\ \dfrac{km}{h}\cdot\dfrac{1000\ m}{1\ km}\cdot\dfrac{1\ h}{3600\ s}=10.71\ \dfrac{m}{s}.$$