27. Acceleration - Rate of Change in Velocity

1. What is Acceleration?

• Definition: Acceleration is the rate of change in velocity. More simply, it describes how quickly an object speeds up or slows down.

• Vector Quantity: Since it is a vector, it has both magnitude and direction.

• Deceleration: A negative acceleration value indicates the object is slowing down.

• Uniform Acceleration: If an object accelerates at a constant rate, it is called uniform or constant acceleration.

2. The Core Acceleration Equation

Use this equation when you are working with time.

\text{Acceleration} (a) = \frac{\text{Change in Velocity} (\Delta v)}{\text{Time} (t)}

• Acceleration ($a$): Measured in meters per second squared (m/s²).

• Change in Velocity ($\Delta v$): This is calculated as v - u.

  • v: Final velocity.

  • u: Initial velocity.

• Time (t): Measured in seconds (s).

3. The Second Equation (Uniform Acceleration)

Use this equation when you are working with distance rather than time.

v^2 - u^2 = 2 \times a \times s

• v: Final velocity (m/s).

• u: Initial velocity (m/s).

• a: Acceleration (m/s²).

• s: Distance (m).

4. Key Values to Remember

• Stationary Objects: If an object starts from rest, its initial velocity ($u$) is $0 \ m/s$.

• Gravity: Objects falling on Earth accelerate downwards at approximately $9.8 \ m/s^2$ due to gravity (ignoring air resistance).

5. Summary Comparison