A dart leaves the barrel of a blowgun at a speed v . The...

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. a. Show that the dart moves inside the barrel for a time of 2$L / v .$ b. If the dart's exit speed is 15.0 $\mathrm{m} / \mathrm{s}$ and the length of the blowgun is $1.4 \mathrm{m},$ show that the time the dart is in the barrel is 0.19 s.

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.
a. Show that the dart moves inside the barrel for a time of 2$L / v .$
b. If the dart's exit speed is 15.0 $\mathrm{m} / \mathrm{s}$ and the length of the blowgun is $1.4 \mathrm{m},$ show that the time the dart is in the barrel is 0.19 s.

Key Concepts

Uniform Acceleration

Uniform acceleration means that the acceleration acting on an object remains constant over the entire period of motion. In physics, this assumption simplifies the analysis of motion, allowing the use of standard kinematic equations to relate displacement, time, velocity, and acceleration. In problems like the dart in a blowgun, assuming uniform acceleration allows an analytical solution to determine the travel time through the barrel.

Kinematic Equations

Kinematic equations are formulas that relate the variables of motion—displacement, initial and final velocities, acceleration, and time—under the assumption of constant acceleration. They play a crucial role in problems involving uniformly accelerated motion by providing a direct way to derive unknown quantities when given sufficient information about the motion conditions, such as the relationship between the final velocity and the distance over which the acceleration occurs.

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