What is Acceleration?
In physics, acceleration ($a$) is the rate at which an object's velocity changes over time. An object is accelerating if it is speeding up, slowing down (this is also called deceleration or negative acceleration), or changing direction.
Like velocity, acceleration is a vector quantity, meaning it has both a magnitude (how much it's changing) and a direction. If a car is traveling north and speeds up, its acceleration is also to the north. If it hits the brakes, its acceleration is to the south, even though it is still moving north.
Acceleration is most commonly measured in meters per second squared (m/s²). This unit means "meters per second, per second." For example, the acceleration due to gravity on Earth ($g$) is approximately 9.8 m/s². This means that, ignoring air resistance, a falling object will increase its speed by 9.8 m/s every second it falls.
The Acceleration Formulas
1. Acceleration from Velocity and Time
The fundamental definition of acceleration is the change in velocity divided by the time it takes for that change to happen.
- $a$: Acceleration, measured in meters per second squared (m/s²).
- $\Delta v$: Change in velocity ($v_f - v_i$).
- $v_f$: Final velocity, in meters per second (m/s).
- $v_i$: Initial velocity, in meters per second (m/s).
- $\Delta t$: The time interval over which the velocity changes, in seconds (s).
2. Acceleration from Force and Mass (Newton's Second Law)
The second main formula for acceleration comes from Newton's Second Law of Motion. It states that the acceleration of an object is directly proportional to the net force ($F$) applied to it and inversely proportional to its mass ($m$).
- $F$: Net force, measured in Newtons (N). (1 N = 1 kg·m/s²)
- $m$: Mass of the object, measured in kilograms (kg).
- $a$: Acceleration, measured in m/s².
This formula tells us two key things: 1) A larger force produces a larger acceleration, and 2) A larger mass (more inertia) resists acceleration more, resulting in a smaller acceleration for the same force.
These two formulas are deeply connected. A force applied over time ($F \Delta t$) causes an impulse, which changes the object's momentum ($m \Delta v$). This change in velocity ($\Delta v$) *is* acceleration in action.
Real-World Examples of Acceleration
- Vehicles: When you press the gas pedal in a car, the engine applies a force that accelerates the car, increasing its velocity. When you hit the brakes, a braking force is applied, causing a negative acceleration (deceleration) that decreases its velocity.
- Gravity: When you drop an apple, the Earth's gravity exerts a constant force on it (its weight). This force causes the apple to accelerate toward the ground at 9.8 m/s².
- Circular Motion: A car driving in a circle at a *constant speed* is still accelerating. Why? Because its *direction* is constantly changing, and a change in velocity (which includes direction) is acceleration. This is called centripetal acceleration, and it's caused by the friction force from the tires turning the car.