Which statement best indicates the particle is slowing down?

Which statement best indicates the particle is slowing down?

• A. v(t) and a(t) have same signs
• B. v(t) = 0
• C. a(t) = 0
• D. v(t) and a(t) have opposite signs

Answer: (D)

Slowing down happens when the force (acceleration) acts opposite to the direction you’re moving (the velocity). Speed is the magnitude of velocity, so its rate of change is the component of acceleration along the velocity direction. When velocity and acceleration point in opposite directions, that component is negative, and the speed decreases. If velocity and acceleration point the same way, the acceleration adds to the velocity and the speed increases. If acceleration is zero, there’s no change in speed—the particle keeps moving at the same speed (though it could move in a straight line at constant velocity). If the velocity is zero at that instant, the speed could begin increasing in the direction of the acceleration, so that doesn’t indicate slowing down.

Slowing down happens when the force (acceleration) acts opposite to the direction you’re moving (the velocity). Speed is the magnitude of velocity, so its rate of change is the component of acceleration along the velocity direction. When velocity and acceleration point in opposite directions, that component is negative, and the speed decreases.

If velocity and acceleration point the same way, the acceleration adds to the velocity and the speed increases. If acceleration is zero, there’s no change in speed—the particle keeps moving at the same speed (though it could move in a straight line at constant velocity). If the velocity is zero at that instant, the speed could begin increasing in the direction of the acceleration, so that doesn’t indicate slowing down.