Answer to Question #138925 in Physics for Hannah

Question

Q1) A city bus leaves the terminal and travels, with a few stops, along a straight route that takes it 12 km [E] of its
starting position in 24 min. In another 24 min, the bus turns around and retraces its path to the terminal.
(a) What is the average speed of the bus for the entire route?
(b) Calculate the average velocity of the bus from the terminal to the farthest position from the terminal.
(c) Find the average velocity of the bus for the entire route.

Answer 1

a) We can find the average speed of the bus for the entire route from the formula:

$$v_{avg} = \dfrac{s}{t} = \dfrac{24 \ km}{48 \ min \cdot(\dfrac{1\ h}{60\ min})}=30\ \dfrac{km}{h}.$$

b) We can find the average velocity from the formula:

$\overrightarrow{v_{avg}}=\dfrac{Displacement}{Time} = \dfrac{12\ km [E]}{24 \ min \cdot(\dfrac{1\ h}{60\ min})} = 30\ \dfrac{km}{h} [E].$

c) We can find the average velocity of the bus for the entire route from the same formula (since the bus returns to the starting position its displacement is equal to zero):

$$\overrightarrow{v_{avg}}=\dfrac{Displacement}{Time} = \dfrac{0\ \dfrac{km}{h}}{48 \ min \cdot(\dfrac{1\ h}{60\ min})}=0\ \dfrac{km}{h}.$$

Answer:

a) $v_{avg} =30\ \dfrac{km}{h}.$

b) $\overrightarrow{v_{avg}}=30\ \dfrac{km}{h} [E].$

c) $\overrightarrow{v_{avg}}=0\ \dfrac{km}{h}.$