The kinetic energy K, in joules, of an object is given by the formula K = 1/2mv^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 = 98v^2, what is the mass of the object, in kilograms?

The kinetic energy K, in joules, of an object is given by the formula K = 1/2mv^2, where m... | SAT Equivalent expressions Practice

Answer: B. $196$

Explanation:

$1$ . Set the two expressions for kinetic energy (K) equal to each other:

- We are given two formulas for K for the same object:

$K = \dfrac{1}{2}mv^2$

$K = 98v^2$

- Therefore:

$\dfrac{1}{2}mv^2 = 98v^2$

$2$ . Solve for the mass, m:

- Since v represents velocity, we can assume $v \ne 0$ , so we can divide both sides by $v^2$ :

$\dfrac{1}{2}m = 98$

- To isolate m, multiply both sides of the equation by $2$ :

$m = 98 \times 2$

$m = 196$

$3$ . Conclusion:

- The mass of the object is $196$ kilograms, which corresponds to option B.