Question

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If the velocity of an object is constant, then its acceleration is zero.

Short answer

The statement 'If the velocity of an object is constant, then its acceleration is zero' is true. Because if an object's velocity is constant (i.e., its speed and direction doesn't change), there is no change in velocity, therefore, the acceleration, which is the rate of change of velocity, is zero.

Step-by-step solution

Understand the definitions of Velocity and Acceleration

Velocity is a quantity that describes the speed and direction of an object's motion. Acceleration, meanwhile, is the rate of change of an object's velocity per unit time.

Analyze the statement

The given statement says that if the velocity of any object is constant, then the object's acceleration is zero. We know that velocity is speed in a particular direction, and a constant velocity implies that the speed and direction remain unchanged over time. Acceleration is the rate of change of velocity - it's how much the velocity changes per unit time. Now, if velocity is constant, that means the velocity is not changing over time. Therefore, since acceleration is the rate of change of velocity and the velocity isn't changing, then the acceleration is zero.

Conclusion

Based on the definitions and analysis of velocity and acceleration, the statement is true. If an object has a constant velocity, that means its speed and direction are not changing with time, so the acceleration, which is the change in velocity, is indeed zero.