College Physics Problem 2.31

A swan on a lake gets airborne by flapping its wings and running on top of the water.
(a) 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 $0.350\:m/s^2$ , how far will it travel before becoming airborne?
(b) How long does this take?

SOLUTION:

Part a.
We are given
$v_0=0$
$v=6.00\:m/s$
$a=0.350\:m/s^2$

From the kinematical equations, the most applicable formula to solve for the change in distance, $\Delta x$ , is $v^2=v_0^2+2a\Delta x$ . Substituting the given values, we have

$\left(6.00\:m/s\right)^2=\left(0\right)^2+2\left(0.350\:m/s^2\right)\Delta x$
$\Delta \:x=\frac{\left(6.00\:m/s\right)^2}{2\left(0.350\:m/s^2\right)}$
$\Delta \:x=51.4286\:m/s^2$