Question

a boat takes off from the dock at 2.5 m/s and speeds up at 4.2 m/s² for 6.0 s. how far has the boat traveled? round your answer to the nearest whole number.

Explanation:

Step1: Identify the kinematic - equation

We use the equation $x = v_0t+\frac{1}{2}at^{2}$, where $v_0$ is the initial velocity, $t$ is the time, and $a$ is the acceleration.

Step2: Substitute the given values

Given $v_0 = 2.5\ m/s$, $a = 4.2\ m/s^{2}$, and $t = 6.0\ s$. Substitute into the equation: $x=(2.5\times6.0)+\frac{1}{2}(4.2)(6.0)^{2}$.

Step3: Calculate the first - term

$2.5\times6.0 = 15$.

Step4: Calculate the second - term

$\frac{1}{2}(4.2)(6.0)^{2}=\frac{1}{2}(4.2)\times36 = 75.6$.

Step5: Calculate the total distance

$x=15 + 75.6=90.6$.

Step6: Round the answer

Rounding 90.6 to the nearest whole number gives 91.

Answer:

91