Question

which statement best describes how velocity and acceleration are related?
acceleration is always negative, and velocity is always positive.
velocity is the rate of change in acceleration.
acceleration is another word for velocity.
acceleration is the rate of change of velocity.

Explanation:

• Acceleration can be positive or negative depending on whether velocity is increasing or decreasing. So, the statement "Acceleration is always negative, and velocity is always positive" is wrong.
• Velocity is not the rate of change of acceleration. The rate of change of acceleration is called jerk.
• Acceleration and velocity are different physical quantities. Velocity is the rate of change of displacement, and acceleration is the rate of change of velocity.
• By definition, acceleration \(a=\frac{\Delta v}{\Delta t}\), where \(\Delta v\) is the change in velocity and \(\Delta t\) is the change in time. So acceleration is the rate of change of velocity.

Answer:

Acceleration is the rate of change of velocity.