Calculating Acceleration
Acceleration = change of velocity ÷ time taken. is the rate of change of velocity. It is the amount that velocity changes per unit time.
What is acceleration? — acceleration definition
Acceleration is the rate of change of an object's speed; in other words, it's how fast velocity changes. According to Newton's second law, acceleration is directly proportional to the summation of all forces that act on an object and inversely proportional to its mass. It's all common sense – if several different forces are pushing an object, you need to work out what they add up to (they may be working in different directions) and then divide the resulting net force by your object's mass.
This acceleration definition says that acceleration and force are, in fact, the same thing. When the force changes, acceleration changes too, but the magnitude of its change depends on the mass of an object (see our magnitude of acceleration calculator for more details). This is not true in a situation when the mass also changes, e.g., in rocket thrust, where burnt propellants exit from the rocket's nozzle. See our rocket thrust calculator to learn more.
We can measure acceleration experienced by an object directly with an accelerometer. If you hang an object on the accelerometer, it will show a non-zero value. Why is that? Well, it's because of gravitational forces that act on every particle that has mass. And where is a net force, there is an acceleration. An accelerometer at rest thus measures the acceleration of gravity, which on the Earth's surface is about 31.17405 ft/s² (9.80665 m/s²). In other words, this is the acceleration due to gravity that any object gains in free fall when in a vacuum.
Speaking of vacuums, have you ever watched Star Wars or another movie that takes place in space? The epic battles of spaceships, the sounds of blasters, engines, and explosions. Well, it's a lie. Space is a vacuum, and no sound can be heard there (sound waves require matter to propagate). Those battles should be soundless! In space, no one can hear you scream.
Example
Calculating Acceleration
Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. The goal of calculating acceleration is to determine how quickly an object is speeding up or slowing down.
The general approach to calculating acceleration includes:
- Identifying the initial and final velocities of the object.
- Knowing the time taken for the change in velocity.
- Applying the formula for acceleration to calculate the result.
Acceleration Formula
The general formula for acceleration is:
\[ a = \frac{{v_f - v_i}}{{t}} \]Where:
- v_f is the final velocity of the object (in meters per second, m/s).
- v_i is the initial velocity of the object (in meters per second, m/s).
- t is the time it takes for the change in velocity (in seconds, s).
Example:
If an object speeds up from 5 m/s to 20 m/s in 3 seconds, the acceleration is:
- Step 1: Subtract the initial velocity from the final velocity: \( v_f - v_i = 20 - 5 = 15 \, \text{m/s} \).
- Step 2: Divide by the time: \( a = \frac{{15}}{{3}} = 5 \, \text{m/s}^2 \).
Acceleration with Changing Direction
Acceleration can also occur when an object changes direction. If the velocity of an object changes direction but not its speed, this is still considered acceleration. For example, an object moving in a circle constantly changes direction, resulting in acceleration even though the speed remains constant.
Example:
If a car turns a corner while maintaining a constant speed of 60 km/h, the car is still experiencing acceleration because its velocity is changing direction, even though the speed is constant.
Real-life Applications of Acceleration
Calculating acceleration has many practical applications, such as:
- Determining how quickly a vehicle can speed up or slow down (e.g., in car safety tests).
- Calculating the acceleration of objects in motion for physics experiments (e.g., determining the acceleration of a falling object).
- Measuring acceleration in sports (e.g., calculating a sprinter's acceleration during a race).
Common Units of Acceleration
SI Unit: The standard unit of acceleration is meters per second squared (\( m/s^2 \)).
Acceleration can also be expressed in other units, such as kilometers per hour squared (\( km/h^2 \)), but the SI unit is commonly used in most calculations.
Common Operations with Acceleration
Uniform Acceleration: When acceleration is constant over time (e.g., an object in free fall near the surface of the Earth).
Variable Acceleration: When the rate of change in velocity is not constant (e.g., a car accelerating in stop-and-go traffic).
Negative Acceleration: Also called deceleration, it occurs when an object slows down over time (e.g., a car braking to stop).
| Problem Type | Description | Steps to Solve | Example |
|---|---|---|---|
| Calculating Acceleration from Velocity | Finding the acceleration when given the initial and final velocities and time. |
|
For an object that speeds up from \( 5 \, \text{m/s} \) to \( 20 \, \text{m/s} \) in 3 seconds, the acceleration is \( a = \frac{{20 - 5}}{{3}} = 5 \, \text{m/s}^2 \). |
| Calculating Deceleration | Finding the negative acceleration (deceleration) when an object is slowing down. |
|
For a car that slows down from \( 30 \, \text{m/s} \) to \( 10 \, \text{m/s} \) in 5 seconds, the deceleration is \( a = \frac{{10 - 30}}{{5}} = -4 \, \text{m/s}^2 \). |
| Calculating Acceleration with Changing Direction | Finding the acceleration when the object changes direction but not speed. |
|
If a car turns a corner with a constant speed of \( 60 \, \text{km/h} \), it experiences acceleration due to the change in direction, even though the speed remains constant. |
| Real-life Applications | Applying acceleration to solve practical problems such as speed, time, and velocity in motion. |
|
If a cyclist accelerates from 0 to \( 12 \, \text{m/s} \) in 6 seconds, use the formula \( a = \frac{{12 - 0}}{{6}} = 2 \, \text{m/s}^2 \) to find the acceleration. |
