How to Find Distance if You Have Velocity and Time

Think About This

The HOUSE Rule

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 $t = \frac{d}{s}$ .

A house that illustrates the relationship between distance, time and velocity

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

Rule

Distance, Speed, Time – the HOUSE Rule

d = s \cdot t t = \frac{d}{s} s = \frac{d}{t}

Rule

Units of Distance, Speed and Time

Distance: meters m or kilometers km,

Time: seconds s or hours h

Then the units of speed are:

\begin{array}{l} km/h & = kilometer per hour \\ m/s & = meters per second \end{array}

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

\begin{array}{l} km/h & = m/s \cdot 3.6 \\ m/s & = km/h \div 3.6 \end{array}

km/h = m/s \cdot 3.6 m/s = km/h : 3.6

Remember that the distance is how far you have moved.

Example 1

A car is driving at a speed of $80 km/h$ . How long does it take to drive $470 km$ ?

\begin{array}{l} t = \frac{d}{s} = \frac{470 km}{80 km/h} = 5.875 h \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 $250 m/s$ . How far will it fly in 3 hours?

\begin{array}{l} 250 m/s \cdot 3.6 & = 900 km/h \\ d & = s \cdot t \\ = 900 km/h \cdot 3 h \\ = 2700 km \end{array}

The plane will fly

2700

km in

3

hours.

Example 3

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

\begin{array}{l} s & = \frac{d}{t} \\ = \frac{100 m}{9.58 s} \\ \approx 10.44 m/s \\ = (10.44 \cdot 3.6) km/h \\ \approx 37.58 km/h \end{array}

He ran at an average speed of

10.44

m/s, which is pretty close to

37.58

km/h!

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