P01R2015 – Trip to the Store

Trip to the Store

Your apartment and the grocery store are both located on the same side of Main Street and are separated by a distance $d=1\ km$. You decide to head out to pick up a few items despite the light rain.

1. To avoid getting too wet, you jog at constant speed to the store and get there in $5\ min$. What is your average velocity? What is your average speed?

\boxed{{\overrightarrow{v}}_{avg}=\frac{\mathrm{\Delta }\overrightarrow{r}}{\mathrm{\Delta }t}=\frac{1000}{5\cdot 60}\ \hat{x}\approx 3.33\ \hat{x}\ \ \ \left(m/s\right)}

\boxed{v_{avg}=\frac{d}{\mathrm{\Delta }t}=\frac{1000}{5\cdot 60}\approx 3.33\ m/s}

2. After purchasing a couple of bags of groceries, you walk home. You initially walk quickly and leave the store with a speed $v_i=2\ m/s$. However, you gradually slow down as you walk toward your apartment and end up reaching it with a speed $v_f=1.2\ m/s$ after $20\ min$. What is your average acceleration?

\mathrm{\Delta }\overrightarrow{v}={\overrightarrow{v}}_f-{\overrightarrow{v}}_i=-2\ \hat{x}-\left(-1.2\ \hat{x}\right)=-0.8\ \hat{x}\ \ \ \ \ \left(m/s\right)

\boxed{{\overrightarrow{a}}_{avg}=\frac{\mathrm{\Delta }\overrightarrow{v}}{\mathrm{\Delta }t}=-\frac{0.8}{20\cdot 60}\ \hat{x}\approx -6.67\times {10}^{-4}\ \hat{x}\ \ \left(m/s^2\right)}

3. What is your average velocity for the return trip? What is your average speed?

\boxed{{\overrightarrow{v}}_{avg}=\frac{\mathrm{\Delta }\overrightarrow{r}}{\mathrm{\Delta }t}=-\frac{1000}{20\cdot 60}\ \hat{x}\approx -0.83\ \hat{x}\ \ \ \left(m/s\right)}

\boxed{v_{avg}=\frac{d}{\mathrm{\Delta }t}=\frac{1000}{20\cdot 60}\approx 0.83\ m/s}

4. Overall, if you consider the entire trip from your apartment to the store and back, and assume that you spent $10\ min$ inside the store, what is your average velocity? What about your average speed? You may neglect any distance walked in the store to pick up your items in front of the distance between your apartment and the store.

\boxed{{\overrightarrow{v}}_{avg}=\overrightarrow{0}\ \ \ \left(m/s\right)}

\boxed{v_{avg}=\frac{2d}{\mathrm{\Delta }t_{tot}}=\frac{2\cdot 1000}{5\cdot 60+10\cdot 60+20\cdot 60}\approx 0.95\ \ m/s}