Speed can increase even if acceleration decreases, as long as the acceleration remains positive and acts in the same direction as the current velocity.
Understanding Acceleration and Speed
In physics, acceleration is defined as the rate of change of velocity over time. Velocity is a vector quantity, meaning it has both magnitude and direction. Speed is the magnitude of velocity.
For an object's speed to increase, its velocity must change in a way that makes its magnitude larger. This happens when there is an acceleration component in the same direction as the object's motion.
The Role of Decreasing Acceleration
The key point is that a decreasing acceleration does not mean the acceleration is zero or negative. It simply means the rate at which velocity is increasing is slowing down.
As stated in the provided reference: "If the acceleration is decreasing but acting in the same direction the rate of increase of velocity will decrease. Consequently the velocity will continue to increase slowly."
Think of it this way:
- Positive acceleration means velocity is increasing.
- Zero acceleration means velocity is constant (speed is constant).
- Negative acceleration (deceleration) means velocity is decreasing.
If the acceleration is positive but its value is getting smaller (e.g., 10 m/s², then 8 m/s², then 5 m/s²), the velocity is still increasing in each time interval. The amount it increases by in each subsequent interval is just less than the previous one.
Visualizing the Concept
Let's look at a simple example starting from rest (initial speed = 0 m/s), where the acceleration is decreasing but always positive and in the direction of motion:
| Time (s) | Acceleration (m/s²) | Velocity Increase in Interval (m/s) | Speed (m/s) |
|---|---|---|---|
| 0 | - | - | 0 |
| 1 | 5 | +5 (0 + 5) | 5 |
| 2 | 3 | +3 (5 + 3) | 8 |
| 3 | 1 | +1 (8 + 1) | 9 |
In this table, the acceleration is decreasing (5 -> 3 -> 1 m/s²). However, because the acceleration is always positive, the speed is continuously increasing (0 -> 5 -> 8 -> 9 m/s). The rate of increase of speed is slowing down, but the speed itself is still going up.
Analogy: A Car Slowing Its Engine Power
Imagine a car starting from a stop. The driver presses the accelerator pedal hard initially, then slowly eases off, but doesn't lift their foot entirely or apply the brake.
- Initial High Acceleration: The car quickly gains speed.
- Decreasing Acceleration: As the driver eases off the pedal (but still keeps it pressed somewhat), the engine is still providing forward thrust, but less than before. The car is still accelerating forward, so its speed is still increasing, but not as rapidly as when the pedal was fully pressed.
- Zero Acceleration: If the driver held the pedal steady, the acceleration might become zero (or constant) once air resistance and friction balance the thrust, and the car would maintain a constant speed.
- Negative Acceleration (Deceleration): If the driver lifted their foot completely or pressed the brake, the acceleration would become negative (opposite the direction of motion), and the car's speed would decrease.
In the scenario where the driver is easing off the pedal but still applying some forward power, the car's acceleration is decreasing, but its speed is still increasing because the net force (and thus acceleration) is still in the forward direction.
Key Takeaway
- Speed increases when acceleration is positive and in the direction of motion.
- Decreasing positive acceleration means the rate at which speed is increasing is slowing down.
- The speed will continue to rise as long as the acceleration remains positive and aligned with the direction of movement, even if its magnitude is diminishing.
This concept is fundamental in understanding motion and the relationship between acceleration, velocity, and speed.
