Question

nova applies a 5 n force to accelerate a toy truck at 12 m/s². ash applies a 15 n force to an identical toy. at what rate does ashs toy accelerate? show your work, or justify your answer.

Explanation:

Step1: Calculate the mass of the toy truck using Nova's data

According to Newton's second law \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. For Nova, \(F_1=5N\) and \(a_1 = 12m/s^{2}\). Rearranging the formula for mass \(m=\frac{F}{a}\), so \(m=\frac{F_1}{a_1}=\frac{5N}{12m/s^{2}}\)

Step2: Use the mass to find Ash's acceleration

The mass of Ash's toy truck is the same as Nova's (\(m=\frac{5}{12}kg\)) since the toys are identical. Ash's force \(F_2 = 15N\). Using \(a=\frac{F}{m}\), substitute \(F = F_2\) and \(m=\frac{5}{12}kg\). Then \(a_2=\frac{F_2}{m}\), substituting \(m=\frac{5}{12}kg\) into the formula gives \(a_2=\frac{15N}{\frac{5}{12}kg}\)

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Another way (using the ratio of forces since \(m\) is constant):
Since \(F = ma\) and \(m\) is constant (\(m=\frac{F_1}{a_1}=\frac{F_2}{a_2}\)), then \(\frac{F_1}{a_1}=\frac{F_2}{a_2}\). Cross - multiply: \(F_1\times a_2=F_2\times a_1\). Solving for \(a_2\): \(a_2=\frac{F_2\times a_1}{F_1}\)

Substitute \(F_1 = 5N\), \(a_1=12m/s^{2}\), \(F_2 = 15N\)

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Answer:

\(36m/s^{2}\)