# Forces: Acceleration

## Forces: Acceleration

### Definition of Acceleration:

• Acceleration is the rate of change of velocity per unit of time. It is a vector quantity which means it has both magnitude and direction.
• Any change in the speed or direction of an object is caused by an acceleration - you can be accelerating even if your speed isn’t increasing!

### Formula for Acceleration:

• The formula for calculating acceleration is: Acceleration (m/s²) = Change in velocity (m/s) ÷ Time taken for the change (s).
• If an object is slowing down rather than speeding up, we say it is decelerating. This is sometimes called negative acceleration.

### Factors Influencing Acceleration:

• The acceleration of an object is directly proportional to the resultant force applied to it. This is expressed in Newton’s Second Law of Motion, which states that Force = mass x acceleration (F = ma).
• Further, the acceleration of an object is inversely proportional to its mass – in other words, the more mass an object has, the less it accelerates in response to a given force.

### Understanding Graphs of Motion:

• In a graph where velocity is plotted against time, the acceleration is given by the slope of the line. A steep slope indicates a large acceleration.
• A horizontal line on a velocity-time graph shows that the object is moving at a steady speed - in other words, it is not accelerating.

### Terminal Velocity:

• Terminal velocity is the highest velocity attainable by an object as it falls freely through a fluid (like air or water).
• It occurs when the downward force of gravity (fg) equals the upward force of drag (fd). This means the net external force on the object is zero, resulting in an acceleration of zero.
• As the acceleration of the object becomes zero, its speed remains constant - that speed is the terminal velocity.

### Free Fall:

• Objects that are falling under the sole influence of gravity experience what is known as free fall.
• In the absence of other forces, all objects near the surface of the Earth will accelerate downwards at a rate of approximately 9.8 m/s², irrespective of their mass. This is known as the acceleration due to gravity.