Yes, it is entirely possible to have an instantaneous speed of zero while still experiencing acceleration. This is a fundamental concept in kinematics, illustrating the difference between velocity (and speed) and acceleration.
Understanding Instantaneous Speed and Acceleration
- Instantaneous Speed: This refers to how fast an object is moving at a precise moment in time. It is the magnitude of the instantaneous velocity.
- Acceleration: This is the rate at which an object's velocity changes over time. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. Therefore, acceleration can occur due to a change in speed, a change in direction, or both.
It's crucial to remember that acceleration describes the change in velocity, not the velocity itself. An object can be momentarily at rest (zero speed) but about to change its state of motion due to an acting force, which implies acceleration.
The Classic Example: A Vertically Thrown Object
The most common and clearest example of this phenomenon is an object thrown straight upward into the air.
- Upward Trajectory: As the object travels upward, its initial upward velocity gradually decreases due to the constant downward pull of gravity.
- At the Peak: When the object reaches the highest point of its trajectory, it momentarily stops moving upward before it begins to fall back down. At this exact instant, its instantaneous vertical velocity (and thus its instantaneous speed) becomes zero.
- Continuous Acceleration: Even at this precise moment when its speed is zero, the object is still under the influence of Earth's gravity. Gravity causes a constant downward acceleration (approximately 9.8 meters per second squared, or $9.8 \text{ m/s}^2$). This acceleration is continuously acting on the object, regardless of its instantaneous velocity. It's this continuous downward acceleration that causes the object to slow down as it rises, momentarily stop, and then accelerate downwards.
This scenario clearly demonstrates that acceleration can be present even when instantaneous speed is zero, as acceleration is about the rate of change of velocity, not the current value of velocity.
Breakdown of Motion for a Thrown Ball
| Phase of Motion | Instantaneous Velocity | Instantaneous Speed | Acceleration (due to gravity) |
|---|---|---|---|
| Rising | Upward (decreasing) | Decreasing | Downward (constant, ~$9.8 \text{ m/s}^2$) |
| Peak | Zero | Zero | Downward (constant, ~$9.8 \text{ m/s}^2$) |
| Falling | Downward (increasing) | Increasing | Downward (constant, ~$9.8 \text{ m/s}^2$) |
Why This Is Possible
The possibility stems from the distinct definitions of velocity and acceleration:
- Velocity describes an object's position change over time.
- Acceleration describes an object's velocity change over time.
An object's velocity can be zero at an instant, but if there's an unbalanced force acting on it (like gravity), that force will cause its velocity to begin changing from that zero state. This change in velocity means there is, by definition, an acceleration. In the case of the thrown ball, gravity is always pulling it, constantly working to change its velocity, even when that velocity is momentarily zero.
Key Takeaway
Acceleration describes how quickly an object's velocity is changing. It's entirely independent of the object's current instantaneous velocity or speed. An object can be momentarily motionless but still be subject to forces that are about to change its state of motion, leading to acceleration.
