# How to Find Distance if You Have Velocity and Time

### TheHOUSERule

Think of a house with a desk $d$ in the attic, and a sofa $s$ and a table $t$ in the living room. Hold your finger over the thing you want to find, for example the time $t$. Then there is a $d$ above an $s$, giving you that $t=\frac{\text{d}}{\text{s}}$.

A house that illustrates the relationship between distance, speed and time. Another word for speed is velocity.

Rule

### Distance,Speed,Time–theHOUSERule

 $d=s\cdot t\phantom{\rule{2em}{0ex}}t=\frac{d}{s}\phantom{\rule{2em}{0ex}}s=\frac{d}{t}$

Rule

### UnitsofDistance,SpeedandTime

Distance: meters m or kilometers km,

Time: seconds s or hours h

Then the units of speed are:

### Converting from m/s to km/h and Vice Versa

$\begin{array}{llll}\hfill \text{km/h}& =\text{m/s}\cdot 3.6\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \text{m/s}& =\text{km/h}÷3.6\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $\text{km/h}=\text{m/s}\cdot 3.6\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\text{m/s}=\text{km/h}:3.6$

Remember that the distance is how far you have moved.

Example 1

A car is driving at a speed of $\text{}80\text{}\phantom{\rule{0.17em}{0ex}}\text{km/h}$. How long does it take to drive $\text{}470\text{}\phantom{\rule{0.17em}{0ex}}\text{km}$?

$\begin{array}{lll}\hfill t=\frac{d}{s}=\frac{470\phantom{\rule{0.17em}{0ex}}\text{km}}{80\phantom{\rule{0.17em}{0ex}}\text{km/h}}=5.875\phantom{\rule{0.17em}{0ex}}\text{h}& \phantom{\rule{2em}{0ex}}& \hfill \end{array}$

Then you need to convert the decimals to find the minutes and seconds.

From the answer you can see that it takes $5$ full hours. To find the number of minutes, multiply the decimal by $60$. That gives you

 $0.875\cdot 60=52.5$

Next, you find the number of seconds:

 $0.5\cdot 60=30$

This means it takes $5$ hours, $52$ minutes and $30$ seconds to drive $470$ km at $80$ km/h.

Example 2

A plane is flying at a speed of $\text{}250\text{}\phantom{\rule{0.17em}{0ex}}\text{m/s}$. How far will it fly in 3 hours?

$\begin{array}{llll}\hfill 250\phantom{\rule{0.17em}{0ex}}\text{m/s}\cdot 3.6& =900\phantom{\rule{0.17em}{0ex}}\text{km/h}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill d& =s\cdot t\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =900\phantom{\rule{0.17em}{0ex}}\text{km/h}\cdot 3\phantom{\rule{0.17em}{0ex}}\text{h}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =2700\phantom{\rule{0.17em}{0ex}}\text{km}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$ The plane will fly $2700$ km in $3$ hours.

Example 3

In 2009, Usain Bolt ran 100 meters in $\text{}9.58\text{}$ seconds. How fast did he run on average? Give the answer in both $\text{m/s}$ and $\text{km/h}$.

$\begin{array}{llll}\hfill s& =\frac{d}{t}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{100\phantom{\rule{0.17em}{0ex}}\text{m}}{9.58\phantom{\rule{0.17em}{0ex}}\text{s}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \approx 10.44\phantom{\rule{0.17em}{0ex}}\text{m/s}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\left(10.44\cdot 3.6\right)\phantom{\rule{0.33em}{0ex}}\text{km/h}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & \approx 37.58\phantom{\rule{0.17em}{0ex}}\text{km/h}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$ He ran at an average speed of $10.44$ m/s, which is pretty close to $37.58$ km/h!