Question

a darts player is throwing new darts at a target to test them out. the player applies the same force to each dart as she is throwing it. order the colors of the darts to show the size of the acceleration each dart will have as it is being thrown.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. Rearranging for acceleration gives \(a=\frac{F}{m}\). Since the force \(F\) is the same for all darts, acceleration \(a\) is inversely proportional to mass \(m\) (\(a\propto\frac{1}{m}\)).

Step2: Compare the masses

The masses of the darts are: blue (\(m_{blue} = 28g\)), green (\(m_{green}=25g\)), gold (\(m_{gold}=23g\)), red (\(m_{red}=29g\)), silver (\(m_{silver}=32g\)).
Since \(a\propto\frac{1}{m}\), the smaller the mass \(m\), the larger the acceleration \(a\).
The order of masses from smallest to largest is \(m_{gold}

Step3: Determine the order of accelerations

Using \(a\propto\frac{1}{m}\), the order of accelerations from largest to smallest (since acceleration is inversely proportional to mass) is: gold, green, blue, red, silver.

Answer:

larger acceleration: gold, green, blue, red, silver : smaller acceleration