Acceleration is the change in speed of a moving object. If an object is moving at a constant speed, there is no acceleration; the latter occurs only when the speed of the object varies. If the speed variation is constant, the object moves with constant acceleration. The acceleration is expressed in meters per second squared and is calculated based on the time it takes for an object to pass from one speed to another in a given interval, or on the basis of an external force applied to the object under study.
Steps
Part 1 of 3: Calculating Acceleration Based on a Force
Step 1. Define Newton's second law relating to motion
This principle states that when the forces exerted on an object are no longer balanced, the object is subject to acceleration. The intensity of the acceleration depends on the net force applied to the object and its mass. Based on this principle, acceleration can be calculated once the intensity of the force applied to the object in question and its mass are known.
- Newton's law is represented by the following equation: F.net = m * a, where Fnet is the total force acting on the object, m is the mass of the object studied and a is the resulting acceleration.
- When using this equation, the metric system must be used as the unit of measurement. Kilograms (kg) are used to express mass, newtons (N) are used to express force and meters per second squared (m / s) are used to describe acceleration.2).
Step 2. Find the mass of the object in question
To find this information, you can simply weigh it using a scale and express the result in grams. If you are studying a very large object, you will most likely have to use a reference source from which to obtain this data. The mass of very large objects is usually expressed in kilograms (kg).
To use the equation given in this guide we need to convert the mass value to kilograms. If the mass value is expressed in grams, simply divide it by 1000 to get the equivalent in kilograms
Step 3. Calculate the net force acting on the object
Net force is the intensity of the unbalanced force acting on the object in question. In the presence of two opposing forces, where one of the two is greater than the other, we have a net force having the same direction as the more intense one. Acceleration occurs when an unbalanced force acts on an object causing its speed to vary in the direction of the force itself.
- Example: Let's say you and your big brother are playing tug of war. You pull the string to the left with a force of 5 Newtons, while your brother pulls it towards him with a force of 7 Newtons. The net force applied to the rope is therefore 2 Newtons to the right, which is the direction your brother is pulling.
- In order to fully understand the units of measurement, know that 1 newton (N) is equal to 1 kilogram-meter per second squared (kg-m / s2).
Step 4. Set the original equation "F = ma" to calculate the acceleration
To do this, divide both sides by the mass thus obtaining the following formula: "a = F / m". To calculate the acceleration, you will simply have to divide the force by the mass of the object subject to it.
- Force is directly proportional to acceleration; that is, a greater force gives a greater acceleration.
- Conversely, mass is inversely proportional to acceleration, so acceleration decreases as mass increases.
Step 5. Use the formula found to calculate the acceleration
We have shown that acceleration is equal to the net force acting on an object divided by its mass. Once you have identified the values of the variables involved, simply perform the calculations.
- Example: a force of 10 Newtons acts uniformly on an object having a mass of 2 kg. What is the acceleration of the object?
- a = F / m = 10/2 = 5 m / s2
Part 2 of 3: Calculating the Average Acceleration based on two Reference Speeds
Step 1. We define the equation that describes the average acceleration
You can calculate the average acceleration of an object over a given time interval based on its initial and final velocity (i.e. the space traveled in a specific direction in a given time). To do this, you need to know the equation that describes acceleration: a = Δv / Δt where a is the acceleration, Δv is the speed variation and Δt is the time interval within which this variation occurs.
- The unit of measurement for acceleration is meters per second squared or m / s2.
- Acceleration is a vector quantity, that is, it has an intensity and a direction. Intensity equals the amount of acceleration imparted to an object, while direction is the direction in which it is moving. If an object is slowing down we will get a negative acceleration value.
Step 2. Understand the meaning of the variables involved
You can define the variables Δv and Δt as follows: Δv = vf - vthe and Δt = tf - tthe, where vf represents the final speed, vthe is the initial velocity, tf is the final time and tthe is the initial time.
- Since acceleration has a direction, it is important that the initial velocity always be subtracted from the final velocity. If the terms of the operation are reversed, the direction of the acceleration would be wrong.
- Unless a different data is provided, normally, the initial time always starts from 0 seconds.
Step 3. Use the formula to calculate the acceleration
First write down the equation of the acceleration calculation and all the values of the known variables. The equation is the following a = Δv / Δt = (vf - vthe) / (tf - tthe). Subtract the initial velocity from the final velocity, then divide the result by the time interval in question. The final result represents the average acceleration over time.
- If the final speed is lower than the initial one, we will get a negative acceleration value, which indicates that the object in question is slowing down its movement.
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Example 1. A racing car accelerates steadily from a speed of 18.5 m / s to 46.1 m / s in 2.47 seconds. What is the average acceleration?
- Take note of the equation for calculating the acceleration: a = Δv / Δt = (vf - vthe) / (tf - tthe).
- Define known variables: vf = 46.1 m / s, vthe = 18.5 m / s, tf = 2.47 s, tthe = 0 s.
- Substitute the values and do the calculations: a = (46, 1 - 18, 5) / 2, 47 = 11, 17 m / s2.
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Example 2. A motorcyclist travels at a speed of 22.4 m / s. In 2, 55 s it stops completely. Calculate its deceleration.
- Take note of the equation for calculating the acceleration: a = Δv / Δt = (vf - vthe) / (tf - tthe).
- Define known variables: vf = 0 m / s, seethe = 22.4 m / s, tf = 2.55 s, tthe = 0 s.
- Substitute the values and do your calculations: a = (0 - 22, 4) / 2, 55 = -8, 78 m / s2.
Part 3 of 3: Check your knowledge
728025 9 1 Step 1. Direction of acceleration
In physics, the concept of acceleration does not always coincide with what we use in everyday life. The acceleration has a direction that is normally represented upwards and to the right, if positive, or downwards and to the left, if negative. Based on the following diagram, check if the solution to your problem is correct:
Behavior of the car How does the speed vary? Direction of acceleration The pilot drives to the right (+) by pressing the accelerator pedal + → ++ (considerable increase) positive The rider drives towards (+) by pressing the brake pedal ++ → + (small increase) negative The pilot drives to the left (-) by depressing the accelerator pedal - → - (considerable decrease) negative The rider drives to the left (-) by depressing the brake pedal - → - (reduced decrease) positive The pilot drives at a constant speed No variations acceleration is 0 
728025 10 1 Step 2. Direction of force
The force generates an acceleration only in its direction. Some problems may try to deceive you by providing you with irrelevant data in order to find the solution.
- Example: a model of a toy boat with a mass of 10 kg accelerates northbound at 2 m / s2. The wind blows from the west, exerting a force of 100 Newtons on the boat. What is the new acceleration of the boat to the north?
- Solution: Since the force of the wind is perpendicular to that of the motion, it has no impact on the object. The boat will then continue to accelerate north at 2 m / s2.
728025 11 1 Step 3. Net Force
If several forces act on the object in question, before you can calculate the acceleration, you will need to combine them correctly to calculate the net force acting on the object. In a two-dimensional space you will have to act like this:
- Example: Luca is pulling a container with a mass of 400 kg to the right by applying a force of 150 Newtons. Giorgio, positioned on the left of the container, is pushing it with a force of 200 newtons. The wind blows from the left exerting a force of 10 newtons. What is the acceleration of the container?
- Solution: This problem uses words to try to confuse your ideas. Draw a diagram of all the forces involved: one to the right by 150 newtons (exerted by Luca), a second always to the right by 200 newtons (exerted by Giorgio) and finally the last one by 10 newtons to the left. Assuming that the direction in which the container is moving is to the right, the net force will be equal to 150 + 200 - 10 = 340 newtons. The acceleration will therefore be equal to: a = F / m = 340 newtons / 400 kg = 0, 85 m / s2.
