Differentiating Uniform and Variable Acceleration
Definition of Acceleration
- Acceleration: Rate of change of velocity ($\frac{dv}{dt}$).
Uniform Acceleration
- Characteristics:
- Change in velocity takes place in the same amount over the same time intervals.
- Equal change in velocity occurs in equal time intervals.
- Example: Motion of a ball under gravity.
- Constant acceleration of 9.8 m/s².
- Acceleration is constant in both magnitude and direction.
Variable Acceleration
- Characteristics:
- Unequal changes in velocity occur over equal time intervals.
- Velocity changes in magnitude or direction (or both) in unequal amounts.
- Example: Motion of a vehicle on a hilly road.
- On hilly roads, the velocity in terms of both magnitude and direction changes at each moment.
Conclusion
- Uniform Acceleration: Constant change; predictable; e.g., gravity.
- Variable Acceleration: Inconstant change; unpredictable; e.g., vehicle on hill.
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