The kinetic energy, in joules, of an object with mass 9 kilograms traveling at a speed of v meters per...

1. TRANSLATE the given information

• Given: \(\mathrm{K(v) = \frac{9}{2}v^2}\) represents kinetic energy function
• We have: \(\mathrm{K(34) = 5,202}\)
• Need to interpret what this equation means in context

2. INFER the meaning of function notation

• In any function \(\mathrm{f(x) = y}\):
  • The value inside parentheses (x) is the input
  • The value after the equals sign (y) is the output
• Therefore in \(\mathrm{K(34) = 5,202}\):
  • 34 is the input value for v (speed in m/s)
  • 5,202 is the output value for K (kinetic energy in joules)

3. TRANSLATE back to context

• The speed is \(\mathrm{v = 34}\) meters per second
• The kinetic energy is \(\mathrm{K = 5,202}\) joules
• So: "The object traveling at 34 meters per second has a kinetic energy of 5,202 joules"

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse which value represents the input and which represents the output in function notation.

They might think \(\mathrm{K(34) = 5,202}\) means "kinetic energy of 34 when speed is 5,202" instead of "kinetic energy of 5,202 when speed is 34." This backwards interpretation of function notation leads them to think the object is traveling at 5,202 m/s with 34 joules of energy.

This may lead them to select Choice C (The object traveling at 5,202 meters per second has a kinetic energy of 34 joules).

The Bottom Line:

Success on this problem depends entirely on correctly interpreting function notation - recognizing that the value in parentheses is always the input (speed) and the value after the equals sign is always the output (kinetic energy).