A dart leaves the barrel of a blowgun at a speed v. The length of the blowgun barrel is L. Assume that the acceleration of the dart in the barrel is uniform. Find a time that the dart moves inside the barrel.
To find the time that the dart moves inside the barrel, we can use the kinematic equation:
v = at
Where:
v = final velocity of the dart (which is the speed it leaves the barrel)
a = acceleration of the dart
t = time the dart moves inside the barrel
The acceleration of the dart can be calculated using the equation:
a = Δv/Δt
Where:
Δv = change in velocity (v - 0 = v)
Δt = change in time (time it takes for the dart to leave the barrel)
Since the acceleration is uniform, we can use the formula for uniform acceleration:
Δv = aΔt
Substitute the values into the equation:
v = aΔt
Solve for t:
t = v/a
Therefore, the time that the dart moves inside the barrel is t = v/a.