Question

1. a skier accelerates uniformly from 5.2 m/s to 12.8 m/s at 0.85 m/s². find the distance the skier travels. (12.8² = 5.2² + 2(0.85)d) a. 7.7 m b. 8.9 m c. 11 m d. 80 m

Explanation:

Step1: Identify the relevant kinematic - equation

The kinematic equation $v^{2}=u^{2}+2as$ is used, where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration and $s$ is the distance. We need to find $s$, so we can re - arrange the formula as $s=\frac{v^{2}-u^{2}}{2a}$.

Step2: Determine the values of $u$, $v$ and $a$

Given $u = 5.2\ m/s$, $v = 12.8\ m/s$ and $a=0.85\ m/s^{2}$.

Step3: Substitute the values into the formula

\[

$$\begin{align*} s&=\frac{v^{2}-u^{2}}{2a}\\ &=\frac{(12.8)^{2}-(5.2)^{2}}{2\times0.85}\\ &=\frac{(12.8 + 5.2)(12.8 - 5.2)}{1.7}\\ &=\frac{(18)\times(7.6)}{1.7}\\ &=\frac{136.8}{1.7}\\ & = 80.47\approx80\ m \end{align*}$$

\]

Answer:

D. 80 m