# A high school athlete runs 1.00 * 10^2 m in 12.20 s. What is the velocity in m/s and km/h?

Jul 6, 2016

$8.20 m {s}^{-} 1$ (3sf) and $29.5 k m {h}^{-} 1$ (3sf)

#### Explanation:

In order to calculate the velocity we need both the distance travelled and the time taken to travel that distance. In this case we have both, I will start by converting the $1.00$ x ${10}^{2}$ into standard form which is $100$m

So $v = \frac{d}{t}$

$d = 100 m$ & $t = 12.20 s$

Substitute both these values into the equation:

$v = \frac{d}{t} = \frac{100 m}{12.20 s} = 8.20 m {s}^{-} 1$

I like to keep the units in the calculation to make working the units of velocity out easier.

Now we know the velocity in $m {s}^{-} 1$. To calculate the speed in $k m {h}^{-} 1$ we need to convert both the $m$ & $s$, this can be done in multiple ways. However we know that $1000 m$ = $1 k m$ and $1$hour = $3600$seconds.

Therefore we need to multiply our answer by: $\frac{1000 m}{3600 s}$ So...

$v = 8.20 m {s}^{-} 1$ x$3.6 = 29.5 k m {h}^{-} 1$

Note: I retained the non-rounded value in the calculator through the calculations, this will improve your accuracy and avoid rounding error.