Question

a bus travels 27 km due east at an average speed of 18 m/s, making stops along the way. the bus then stops at the bus station for 55 minutes for a lunch break and then continues due east another 11 km for 7 minutes. what is the buss average velocity over this entire drive?
24.3 m/s east
10.2 m/s east
7.28 m/s east
1.63 m/s east

Explanation:

Step1: Calculate the time for the first part of the journey

The formula for time \(t=\frac{d}{v}\). Given \(d = 27\times10^{3}\text{ m}\) and \(v = 18\text{ m/s}\).
\(t_{1}=\frac{27\times 10^{3}}{18}=1500\text{ s}\)

Step2: Convert all time units to seconds

The stop time \(t_{2}=55\times60 = 3300\text{ s}\), and the third - part time \(t_{3}=7\times60=420\text{ s}\)
The total displacement \(d_{total}=(27 + 11)\times10^{3}=38\times10^{3}\text{ m}\)
The total time \(t_{total}=t_{1}+t_{2}+t_{3}=1500 + 3300+420=5220\text{ s}\)

Step3: Calculate the average velocity

The formula for average velocity \(v_{avg}=\frac{d_{total}}{t_{total}}\)
\(v_{avg}=\frac{38\times 10^{3}}{5220}\approx7.28\text{ m/s}\)

Answer:

7.28 m/s East