Acceleration is the rate at which an object’s velocity changes. If you are speeding up, slowing down, or changing direction, you are accelerating. It is the “how quickly?” question for velocity.

What is Acceleration?

Acceleration is the rate at which an object’s velocity changes. This change can be in:

  1. Speed: The object is speeding up or slowing down.
  2. Direction: The object is changing its path (even if its speed is constant).

Since velocity is a vector quantity (having both magnitude and direction), a change in either its magnitude (speed) or its direction (or both) means there is acceleration.

  • Key Idea: “How quickly is its velocity changing?”
  • Nature: Acceleration is a vector quantity. It has both magnitude and direction.
  • Symbol: We often use the symbol $a$.
  • Formula: Average acceleration is calculated as the change in velocity divided by the change in time: \(\text{Average Acceleration} = \frac{\text{Change in Velocity}}{\text{Change in Time}} = \frac{\Delta v}{\Delta t}\)
  • Units: Meters per second squared (m/s²) in the SI system. This means “meters per second, per second” – for example, an acceleration of 2 m/s² means the velocity changes by 2 m/s every second.

Understanding Direction of Acceleration

The direction of acceleration is not always the same as the direction of motion.

  • Speeding Up: If an object is speeding up, its acceleration is in the same direction as its velocity.
    • Example: A car moving right and speeding up has acceleration to the right.
    • Example: A car moving left and speeding up has acceleration to the left.
  • Slowing Down: If an object is slowing down, its acceleration is in the opposite direction to its velocity.
    • Example: A car moving right and slowing down has acceleration to the left.
    • Example: A car moving left and slowing down has acceleration to the right.
  • Changing Direction (even at constant speed): An object moving in a circle at a constant speed is still accelerating because its direction of velocity is constantly changing. The acceleration here is directed towards the center of the circle.

Interactive Acceleration Visualizer

Select a motion scenario to observe how velocity (green arrow) and acceleration (red arrow) vectors behave on a number line.

Position: --- m

Velocity: --- m/s

Acceleration: --- m/s²

Select a motion type to see how velocity and acceleration vectors behave!

Constant vs. Non-Constant Acceleration

  • Constant Acceleration: This means the velocity changes by the same amount in every equal time interval. On a velocity-time graph, this is represented by a straight line with a constant slope.
  • Zero Acceleration: If an object has zero acceleration, its velocity is constant (not changing). This means it’s either at rest or moving at a steady speed in a straight line.
  • Non-Constant Acceleration: This means the velocity changes at a varying rate. On a velocity-time graph, this is represented by a curved line.

Why This Matters?

Acceleration is a cornerstone of kinematics because:

  • It allows us to predict how an object’s velocity will change over time.
  • It’s crucial for understanding the forces that cause motion (though we won’t discuss forces here).
  • It helps describe complex motions, from a falling apple to planets orbiting the sun.

Interactive Match: Acceleration

Test your understanding of key terms related to acceleration by matching them with their meanings.

Click a term and then its matching meaning. Match all pairs to complete!

💡 Quick Concept Check:

A car is traveling at 20 m/s to the East. It then brakes and slows down to 10 m/s, still heading East. In what direction is the car's acceleration?

Click to Reveal Answer
The car is moving East but slowing down. When an object slows down, its acceleration is in the **opposite direction** to its velocity. Therefore, the car's acceleration is to the **West**.
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