Question

# If you are driving 110 km/h along a straight road and you look to the side for 2.0 s, how far do you travel during this inattentive period?

Solution

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Starting with the information we have in the text of the exercise

\begin{align*} v&=110 \, \dfrac{\text{km}}{\text{h}} \\ t&=2 \, \text{s} \end{align*}

The relation between speed, distance and time is given by equation (1)

$\begin{equation} s=v\cdot t \end{equation}$

However, before inserting the numbers into the equation we observe that we have incompatible units. Specifically, time is in the seconds, while velocity is in kilometers per hour. One of the ways to resolve this would be to simply convert units of speed to meters per second.

$v=110 \, \dfrac{1000 \, \text{m}}{3600 \, \text{s}}\approx 30.5 \, \dfrac{\text{m}}{\text{s}}$

where we used

\begin{align*} 1 \, \text{km}&=1000 \, \text{m}\\ 1 \, \text{h}&=3600 \, \text{s} \end{align*}

Finally, inserting the numbers into the equation (1)

\begin{align*} s&=30.5 \, \dfrac{\text{m}}{\text{s}} \cdot 2 \, \text{s} \\ \end{align*}

$\boxed{s=61 \, \text{m}}$

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