## 116. Math Puzzle $1 / 75$

A bobsled crosses the starting line with an initial speed of $18 \mathrm{~km} / \mathrm{h}$ and receives a constant acceleration of $0.8 \mathrm{~m} / \mathrm{s}^{2}$.

When and where does it reach a speed of $90 \mathrm{~km} / \mathrm{h}$?
The speed of $90 \mathrm{~km} / \mathrm{h}$ is reached after $t$ seconds. It holds that ($v_{0}$ initial speed $=18 \mathrm{~km} / \mathrm{h}$

$$
v_{0}+a \cdot t=v_{\text{End}}=90 \mathrm{~km} / \mathrm{h}
$$

When the quantities are referred to $\mathrm{m}$ and s, we get the numerical equation

$$
5 \times 0.8 t=25 \quad ; \quad t=25 \mathrm{~s}
$$

The speed $v_{\text{End}}=90 \mathrm{~km} / \mathrm{h}$ is reached $x \mathrm{~m}$ behind the starting line

$$
v_{0} \cdot t+\frac{1}{2} a t^{2}=x
$$

where $t=25 \mathrm{~s}$. When the quantities are referred to $\mathrm{m}$ and $\mathrm{s}$, we get the numerical equation

$$
5 \cdot 25+\frac{1}{2} \cdot 0.8 \cdot 625=375
$$

$x=375 \mathrm{~m}$

The racing sled reaches the speed of $90 \mathrm{~km} / \mathrm{h}$ 25 seconds after the start and $375 \mathrm{~m}$ behind the starting line.