Question

the kinetic energy k, in joules, of an object is given by the formula ( k=\frac{1}{2}mv^{2} ), where m is 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 = 34v^{2} ), what is the mass of the object, in kilograms?
a 17
b 34
c 68
d 1,156

Explanation:

Step1: Equate the two kinetic - energy formulas

Given \(K=\frac{1}{2}mv^{2}\) and \(K = 34v^{2}\). So, \(\frac{1}{2}mv^{2}=34v^{2}\).

Step2: Solve for \(m\)

Since \(v
eq0\) (if \(v = 0\), the object has no motion and kinetic energy, but in the context of the formula comparison, we can divide both sides of the equation \(\frac{1}{2}mv^{2}=34v^{2}\) by \(v^{2}\). We get \(\frac{1}{2}m=34\). Then multiply both sides by \(2\): \(m=34\times2\).

Answer:

C. 68