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Acceleration is the rate of change in velocity during the motion of an object. [1] X Research Source When maintaining a constant velocity, the object does not accelerate. Acceleration occurs only when there is a change in velocity. When the velocity varies by a fixed degree, the object is moving with a constant acceleration [2] X Research Source . You can calculate acceleration in meters/second/second, based on the time it takes to go from one velocity to another, or based on the object’s mass.
Steps
Calculate acceleration from a force
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Understand Newton’s second law of motion. Newton’s second law of motion states that when an object is acted upon by forces of nonzero net force, the object will accelerate. This acceleration depends on the total external force acting on the object and its mass. [3] X Source of Research With this law, we can calculate acceleration when we know the force acting on an object of a given mass.
- Newton’s law can be expressed by the equation F net = mxa , where F net is the total external force acting on the object, m is the mass of the object and a is its acceleration.
- When using this equation, use metric units. Use kilograms (kg) for mass, newtons (N) for force, and meters per second squared (m/s 2 ) for acceleration.
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Find your object’s mass. To find the mass of an object, we simply put it on a scale and find the mass in grams. If it’s a very large object, you may have to find a reference object to determine its mass. Large objects usually have mass in kilograms (kg).
- With this equation, you should convert mass to kilograms. If you have a mass in grams, to convert it to kilograms, just divide it by 1000.
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Calculate the total external force acting on your object. The total external force is an unbalanced force. If there are two forces in opposite directions and one is greater than the other, their resultant will be in the direction of the larger force. [4] X Research Source Acceleration occurs when an unbalanced force acts on an object, causing it to change speed in the direction of the push or pull of that force.
- For example: Let’s say you and your brother are playing tug of war. You pull the rope to the left with a force of 5 newtons while your brother pulls it in the opposite direction with a force of 7 newtons. The total external force acting on the rope is 2 newtons to the right, your brother’s direction.
- To understand the unit of measure well, you need to know that 1 newton (N) is equal to 1 kilogram X meters/second squared (kg X m/s 2 ). [5] X Research Sources
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Rearrange the equation F = ma to find a. You can transform this formula to find the acceleration by dividing both sides by the mass. Then we have: a = F/m. To find the acceleration, we simply divide the force by the mass of the object being accelerated.
- Force is directly proportional to acceleration, that is, the greater the force, the greater the acceleration.
- Mass is inversely proportional to acceleration, that is, the larger the mass, the less acceleration.
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Use the formula to find the acceleration. Acceleration is equal to the sum of the external forces acting on an object divided by its mass. Once you’ve determined the variables, do this simple division to find the object’s acceleration.
- For example: A force of 10 Netwon uniformly acts on an object of mass 2 kg. What is the object’s acceleration?
- a = F/m = 10/2 = 5 m/s 2
Calculate the average acceleration from the two velocities
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Determine the average acceleration equation. You can calculate the average acceleration of an object over a period of time based on its velocity (how fast it moves in a particular direction) before and after that time interval. To do so, you need to know the acceleration equation: a = Δv / Δt , where a is the acceleration, Δv is the change in velocity, and Δt is the time it took to get that change. [6] X Research Sources
- The unit of acceleration is meters per second per second or m/s 2 .
- Acceleration is a vector quantity, meaning it has both magnitude and direction. [7] X Research Source The magnitude of the acceleration is the total amount of acceleration, and the direction is the path of the object’s movement. As the object slows down, we have negative acceleration.
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Understand variables. You can define Δv and Δt more carefully: Δv = v f – v i and Δt = t f – t i , where v f is the final velocity, v i is the initial velocity, t f is the time end and t i is the start time. [8] X Research Sources
- Since acceleration is a directional quantity, it is extremely important to always subtract the initial velocity from the final velocity. If you do the opposite, the direction of the acceleration will be incorrect.
- Unless the problem dictates otherwise, the start time is usually 0 seconds.
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Use the acceleration formula. First, write down your equation and any known variables. The equation is a = Δv / Δt = (v f – v i )/(t f – t i ) . Take the difference between the final velocity and the initial speed and divide the result by the time interval. The end result is the average acceleration during that time.
- If the final velocity is less than the initial velocity, the acceleration will be a negative quantity or it is the slowing down of the object.
- Example 1: A car accelerates steadily from 18.5 m/s to 46.1 m/s within 2.37 seconds. What is its average acceleration?
- Write the equation: a = v / t = (v f – v i )/(t f – t i )
- Determine the variables: v f = 46.1 m/s, v i = 18.5 m/s, t f = 2.47 s, t i = 0 s.
- Solution: a = (46.1 – 18.5)/2.47 = 11.17 m/s 2 .
- Example 2: A motorcyclist traveling at a speed of 22.4 m/s applies the brake and stops after 2.55 s. Find the person’s acceleration.
- Write the equation: a = v / t = (v f – v i )/(t f – t i )
- Determine the variables: v f = 0 m/s, v i = 22.4 m/s, t f = 2.55 s, t i = 0 s.
- Solution: a = (0 – 22.4)/2.55 = -8.78 m/s 2 .
Test your knowledge
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The direction of the acceleration. The physical concept of acceleration does not always coincide with the way we use the term in everyday life. Every acceleration has a direction, usually positive when it’s UP or RIGHT and negative when it’s DOWN or LEFT. Check to see if your answer makes sense with the following analysis:
| Expression of the car | How does the speed change? | Direction of acceleration |
|---|---|---|
| Driving to the right (+) press the gas | + → ++ (increase in the right direction) | positive |
| Drive the car to the right (+) apply the brake | ++ → + (decrease in the right direction) | minus |
| Driving to the left (-) press the gas | – → — (increase in the left direction) | minus |
| Driving to the left (-) press the brake | — → – (decrease in the left direction) | minus |
| Driving the car moving at a constant speed | keep stable | zero acceleration |
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Direction of force. Remember, a force only causes acceleration in the direction of that force . Some math problems will try to trick you with irrelevant values.
- Example Problem: A 10 kg toy boat is accelerating north with an acceleration of 2 m/s 2 . A westerly wind exerts a force of 100 N on the boat. What is the boat’s new northward acceleration?
- Solution: Since the force of the wind is perpendicular to the direction of motion, it has no effect on the motion of the boat in that direction. The boat continues to accelerate northward with an acceleration of 2 m/s 2 .
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Total external force. If the object is subjected to more than one force, combine them into the total external forces before calculating the acceleration. In a two-dimensional problem, it would look like this:
- Example Problem: A pulls a 400 kg container to the right with a force of 150 newtons. B stands to the left of the container and pushes it with a force of 200 newtons. The westerly wind blows with a force of 10 newtons. What is the acceleration of the container?
- Solution: This problem uses tricky language to try to fool you. Draw a graph and you will see that the forces acting on the container include 150 newtons to the right, 200 newtons to the right and 10 newtons to the left. If “must” is positive, our total force is 150 + 200 – 10 = 340 newtons. Acceleration = F / m = 340 newtons / 400 kg = 0.85 m/s 2 .
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wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 37 people, some of whom are anonymous, have edited and improved the article over time.
There are 8 references cited in this article that you can see at the bottom of the page.
This article has been viewed 187,697 times.
Acceleration is the rate of change in velocity during the motion of an object. [1] X Research Source When maintaining a constant velocity, the object does not accelerate. Acceleration occurs only when there is a change in velocity. When the velocity varies by a fixed degree, the object is moving with a constant acceleration [2] X Research Source . You can calculate acceleration in meters/second/second, based on the time it takes to go from one velocity to another, or based on the object’s mass.
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