Question

a swan on a lake gets airborne by flapping its wings and running on top of the water. if the swan must reach a velocity of 6.00 m/s to take off and it accelerates from rest at an average rate of 0.350 m/s², how far will it travel before becoming airborne?
if your answer is not an integer, write it to 3 significant figures in standard decimal form.
______ m
your answer

Explanation:

Step1: List known variables

Initial velocity $v_0 = 0\ \text{m/s}$, final velocity $v = 6.00\ \text{m/s}$, acceleration $a = 0.350\ \text{m/s}^2$

Step2: Select kinematic equation

Use $v^2 = v_0^2 + 2ax$, solve for $x$:
$$x = \frac{v^2 - v_0^2}{2a}$$

Step3: Substitute values into formula

$$x = \frac{(6.00)^2 - 0^2}{2\times0.350} = \frac{36.0}{0.700}$$

Step4: Calculate final value

$$x = 51.428... \approx 51.4$$

Answer:

51.4 m