To find out how long the foam dart was in the barrel of the Nerf gun, we need to use some basic physics principles. We can start with Newton’s second law, which states that force equals mass times acceleration (F = ma). We also know the relationship between acceleration and velocity.
First, we need to convert the mass of the dart from grams to kilograms since the standard unit of mass in physics is kilograms. The mass of the dart is 16 grams, which is equal to:
Mass (m) = 16 g = 0.016 kg
Next, we can use the formula for force:
F = m * a
Given that the average force (F) is 192 N, we can rearrange the formula to find the acceleration (a):
a = F / m = 192 N / 0.016 kg = 12000 m/s²
Now that we know the acceleration of the dart, we can use the kinematic equation that relates velocity, acceleration, and time:
v = a * t
Where:
v = exit velocity (12 m/s)
a = acceleration (12,000 m/s²)
t = time in seconds
We can rearrange this formula to solve for time (t):
t = v / a = 12 m/s / 12000 m/s² = 0.001 s
To convert seconds into milliseconds, we multiply by 1000:
t = 0.001 s * 1000 = 1 ms
Therefore, the foam dart was in the barrel of the Nerf gun for approximately 1 millisecond.