Question

the mass of the object, in kilograms, and v is the velocity of the object, in meters per second. if the kinetic energy of a certain object can be found by using the formula k = 56v², what is the mass of the object, in kilograms?
a 28
b 56
c 112
d 3,136

Explanation:

1. Recall the kinetic - energy formula:

• The correct kinetic - energy formula is \(K=\frac{1}{2}mv^{2}\). In the given problem, it seems there is a mis - typing and it should be \(K = \frac{1}{2}mv^{2}\). Let's assume we are given values of \(K\) and \(v\) and we need to solve for \(m\).
• First, start with the formula \(K=\frac{1}{2}mv^{2}\).
• Multiply both sides of the equation by \(2\) to get rid of the fraction:
• \(2K = mv^{2}\).
• Then, divide both sides of the equation by \(v^{2}\) to solve for \(m\):
• \(m=\frac{2K}{v^{2}}\).
• However, since the values of \(K\) and \(v\) are not given in the problem statement, we can't calculate a numerical answer. But if we assume for the sake of showing the process that \(K = 56\) and \(v = 2\):
• Substitute \(K = 56\) and \(v = 2\) into the formula \(m=\frac{2K}{v^{2}}\).
• First, calculate the denominator \(v^{2}=2^{2}=4\).
• Then, calculate the numerator \(2K = 2\times56 = 112\).
• So, \(m=\frac{112}{4}=28\).

Answer:

A. 28