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Solved Problem on Kinematics

A worker leaves his house and walks for 600 meters in 5 minutes to the bus stop, as soon as he reaches the bus stop he takes the bus and travels for 40 minutes at a constant speed of 18 kilometers per hour to the factory where he works. If he took the entire route by bike, at a constant speed of 6 meters per second, how long would it take from home to the factory? Answer in minutes.

Problem data

- distance from the house to the bus stop: Δ
*S*_{1}= 600 m; - the time interval from house to bus stop: Δ
*t*_{1}} = 5 min; - the time interval from the bus stop to the factory: Δ
*t*_{2}= 40 min; - speed of the bus:
*v*o_{}= 18 km/h; - speed of the bicycle:
*v*_{3}= 6 m/s.

We choose a frame of reference oriented to the right (figure 1)

Solution

Converting the given time intervals in minutes to seconds and the bus speed given in kilometers per hour to meters per second used in the

\[
\Delta t_{1}=5\;\cancel{\text{min}} \times \frac{60\;\text{s}}{1\;\cancel{\text{min}}}=300\;\text{s}\\
{}\\
\Delta t_{2}=40\;\cancel{\text{min}} \times \frac{60\;\text{s}}{1\;\cancel{\text{min}}}=2400\;\text{s}\\
{}\\
v_{2}=18\;\frac{\cancel{\text{km}}}{\cancel{\text{h}}} \times \frac{1000\;\text{m}}{1\;\cancel{\text{km}}} \times \frac{1\;\cancel{\text{h}}}{3600\;\text{s}}=\frac{18}{3,6}\;\frac{\text{m}}{\text{s}}=5\;\text{m/s}
\]

\[
\Delta S=\Delta S_{1}+\Delta S_{2} \tag{I}
\]

the foot displacement is already given in the problem Δ

\[
v_{2}=\frac{\Delta S_{2}}{\Delta t_{2}}\\
\Delta S_{2}=v_{2}\;\Delta t_{2}\\
\Delta S_{2}=5 \times 2400\\
\Delta S_{2}=12000\;\text{m}
\]

From expression (I) the total displacement will be
\[
\Delta S=600+12000\\
\Delta S=12600\;\text{m}
\]

as the speed of the bicycle is constant, we use the expression of the average speed to know the total time of
the route Δ
\[
v_{3}=\frac{\Delta S}{\Delta t}\\
\Delta t=\frac{\Delta S}{v_{3}}\\
\Delta t=\frac{12600}{6}\\
\Delta t=2100\;\text{s}
\]

converting this value to minutes, we have
\[
\Delta t=2100\;\cancel{\text{s}} \times \frac{1\;\text{min}}{60\;\cancel{\text{s}}}=35\;\text{min}
\]

\[ \bbox[#FFCCCC,10px]
{\Delta t=35\;\text{min}}
\]

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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .