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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