An experiment was done to determine a student's reaction time. Student A placed a meter stick between two of Student B's fingers. Student A called out when she let go of the meter stick. Student B caught the meter stick. Calculate reaction time?

Oct 21, 2014

$t = \sqrt{\frac{2 d}{g}}$

Explanation:

The equation to determine your reaction time is derived from the kinematic formula:

$d$$=$$\frac{1}{2} \cdot g \cdot {t}^{2}$,

where:

$d$ = the distance the meter stick fell, in meters (divide cm by 100)
$g$ = the acceleration of gravity, ${\text{9.81 m/s}}^{2}$
$t$ = the time the meter stick fell, in seconds

To derive the formula for determining reaction time from the previous equation:

1) multiply both sides times 2;

$2 \cdot d = \cancel{2} \cdot \frac{1}{\cancel{2}} \cdot g \cdot {t}^{2}$

$2 d = g \cdot {t}^{2}$

2) divide both sides by $g$;

$\frac{2 d}{g} = \cancel{g} \cdot {t}^{2} / \cancel{g}$

3) take the square root of both sides.

$\sqrt{\frac{2 d}{g}} = t$

Switch sides.

$t = \sqrt{\frac{2 d}{g}}$