A Simple Reaction-Time Test.? A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. When you see the meter stick released, you grab it with those two fingers. You can calculate your reaction time from the distance the meter stick falls, read directly from the point where your fingers grabbed it. (a) Derive a relationship for your reaction time in terms of this measured distance, d. (b) If the measured distance is 17.6 cm, what is your reaction time?
Solution 41E a) As the meter stick falls and you read the distance it falls as “d”. Because of the acceleration due to gravity, the stick falls and let’s calculate the time it takes to fall a distance of “d”. From the equation of motion, 2 2 d = ut + 1/2 at = 1/2 at [as initial speed was zero] 2 t = 2gd t = 2d------------------------(1) At this much time you caught the stick again between your fingers. 2 We know the value of g , which is 9.8 m/s . let’s put it in eqn (1) t = 2 × 9.8 × d = 4.42 × d1/2. CONCLUSION: So, the relationship between your reaction time and the distance is, t = 19.6 × d. b) If the distance d=17.6 cm=0.176 meters. Reaction time will be, t = 19.6 × d = 19.6 × 0.176 = 3.45 = 1.86 s. CONCLUSION: The reaction time would be 1.86 s if the distance is 17.6 cm.