Which of the following statements about kinetic energy is incorrect?

• A. An object at rest has zero kinetic energy.
• B. The kinetic energy of an object is given by $0.5\times m\times v^2$.
• C. Kinetic energy depends on both the mass and the speed of an object.
• D. Kinetic energy can be negative if the velocity is negative.

Answer: (D)

Verified step by step guidance

1. Recall the definition of kinetic energy, which is the energy an object possesses due to its motion. The formula for kinetic energy is given by \( KE = 0.5 \times m \times v^{2} \), where \(m\) is the mass and \(v\) is the velocity of the object.
2. Understand that kinetic energy depends on the mass and the square of the velocity. Since velocity is squared, the kinetic energy is always non-negative regardless of the direction of velocity.
3. Analyze the statement 'An object at rest has zero kinetic energy.' Since velocity \(v = 0\) for an object at rest, substituting into the formula gives \(KE = 0\), so this statement is correct.
4. Consider the statement 'Kinetic energy depends on both the mass and the speed of an object.' Since kinetic energy is proportional to mass and the square of velocity (speed), this statement is also correct.
5. Evaluate the statement 'Kinetic energy can be negative if the velocity is negative.' Because velocity is squared in the kinetic energy formula, even if velocity is negative, \(v^{2}\) is positive, making kinetic energy always zero or positive. Therefore, this statement is incorrect.