If you've ever seen another car speeding past your car after a red light, then you've experienced the difference in acceleration firsthand. Acceleration is the rate at which an object's velocity changes as it moves. You can calculate acceleration, expressed in meters per second per second, based on the time it takes an object to change its speed, or based on the force exerted on the object.
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Method 1 of 3: Calculating Acceleration from Force
Step 1. Understand Newton's second law of motion
Newton's second law of motion states that when the force exerted on an object is unbalanced, the object will accelerate. This acceleration is determined by the resultant force on the object, as well as the mass of the object itself. Acceleration can be calculated if the force exerted on an object and the mass of the object are known.
- Newton's laws can be translated into equations Fnet = m x a, with Fnet Expresses the resultant force on the object, m the mass of the object, and a the acceleration on the object.
- Use metric units when using this equation. Use the kilogram (kg) as the unit of mass, Newton (N) as the unit of force, and meters per second squared (m/s2) to express acceleration.
Step 2. Determine the mass of the object
To find out the mass of an object, you can weigh it on a balance and record its weight in grams. If the object you have is very large, you may need a reference to find out its mass. Large objects usually have a weight in kilograms (kg).
You must convert the units of mass to kilograms to continue calculations with this equation. If the mass of your object is expressed in grams, you only need to divide that value by 1000 to convert it to kilograms
Step 3. Calculate the resultant force on the object
The resultant force is an unbalanced force. If there are two forces that are opposite to each other, and one is greater than the other, the resultant of the two forces will be the same as the direction of the larger force. Acceleration occurs when an object experiences an unbalanced force, so that its speed changes to approach the force that is pulling or pushing it.
- For example: let's say you and your sister are playing tug of war. You pull the rope to the left with a force of 5 Newtons, while your brother pulls the rope in the opposite direction with a force of 7 Newtons. The resultant force on the string is 2 Newtons to the left, towards your brother.
- In order to understand the units better, understand that 1 Newton (1 N) equals 1 kilogram-meter/second squared (kg-m/s2).
Step 4. Change the equation F = ma to solve the acceleration problem
You can change the order of the formula to calculate acceleration, by dividing both sides of the equation by the mass, so you get the equation: a = F/m. To find acceleration, you just need to divide the force by the mass of the object experiencing it.
- The force is directly proportional to the acceleration, which means, the greater the force experienced by an object, the acceleration will be even greater.
- Mass is inversely proportional to acceleration, which means, the more mass an object has, the less acceleration it will have.
Step 5. Use the formula to solve the acceleration problem
Acceleration is equal to the resultant force on an object divided by its mass. Once you've written down the known variables, do the division to find the object's acceleration.
- For example: a force of 10 Newtons is exerted in the same direction on an object of mass 2 kg. What's the acceleration?
- a = F/m = 10/2 = 5 m/s2
Method 2 of 3: Calculating the Average Acceleration of Two Speeds
Step 1. Determine the equation for the average acceleration
You can calculate the average acceleration of an object over a certain period of time based on its velocity (the speed of the object in a certain direction), before and after that time span. To calculate it, you need to know the equation for calculating acceleration: a = v / t where a represents the acceleration, v the change in velocity, and t the time it takes to change the object's velocity.
- The unit of acceleration is meters per second per second, or m/s2.
- Acceleration is a vector quantity, which means it has both magnitude and direction. The magnitude of the acceleration is the total amount, while its direction is determined by the direction in which the object is moving. If the object slows down, the acceleration will be negative.
Step 2. Understand the variables
You can determine v and t by further calculations: v = vf - vi and t = tf - ti with vf represents the final velocity, vi initial speed, tf end time, and ti initial time.
- Since acceleration has a direction, you should always reduce the final velocity to the initial velocity. If you reverse it, the direction of acceleration you get will be wrong.
- Unless otherwise stated in the problem, the initial time the object moves is usually 0 seconds.
Step 3. Use the formula to find the acceleration
First, write down your equation along with all the known variables. The equation is a = v / t = (vf - vi)/(tf - ti). Subtract the final speed by the initial speed, then divide the result by the time span. The result is the object's average acceleration over that time span.
- If the object's final velocity is less than its initial velocity, the acceleration will be negative, meaning the object is decelerating.
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Example 1: the speed of a race car increases constantly from 18.5 m/s to 46.1 m/s in 2.47 seconds. What is the average acceleration?
- Write the equation: a = v / t = (vf - vi)/(tf - ti)
- Write down the known variables: vf = 46, 1 m/s, vi = 18.5 m/s, tf = 2, 47 s, ti = 0 s.
- Solve the equation: a = (46, 1 – 18, 5)/2, 47 = 11, 17 meters/second2.
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Example 2: a cyclist stops at 22.4 m/s after 2.55 seconds of pressing the brake. Determine the deceleration.
- Write the equation: a = v / t = (vf - vi)/(tf - ti)
- Write down the known variables: vf = 0 m/s, vi = 22.4 m/s, tf = 2.55 s, ti = 0 s.
- Solve the equation: a = (0 – 22, 4)/2, 55 = -8, 78 meters/second2.
Method 3 of 3: Rechecking the Answers
Step 1. Direction of acceleration
The concept of acceleration in physics is not always in accordance with what is used in everyday life. Each acceleration has a direction, usually indicated by a positive symbol if it is pointing up or to the right, or negative if it is headed down or to the left. Double-check that your answer makes sense based on the instructions below:
| Car Movement | Car Speed Change | Acceleration Direction |
|---|---|---|
| Move to the right (+) press the gas pedal | + → ++ (faster) | positive |
| Move to the right (+) press the brake | ++ → + (less positive) | negative |
| Move left (-) press the gas pedal | - → -- (more negative) | negative |
| Move left (-) press brake | -- → - (less negative) | positive |
| Moving at a constant speed | remains the same | acceleration is zero |
Step 2. Style direction
Remember, a force only causes an acceleration "in the direction of the force". Some questions may trick you with scores that are not related to acceleration.
- Example problem: a toy ship with a mass of 10 kg is moving with an acceleration to the north of 2 m/s2. The wind blows the ship westward with a force of 100 Newtons. What is the acceleration of the ship heading north after being blown by the wind?
- Answer: because the direction of the force is perpendicular to the object's motion, it has no effect on objects moving in that direction. The ship will continue to move towards the north with an acceleration of 2 m/s2.
Step 3. Resultant style
If the force experienced by an object is more than one, calculate the resultant force from all of them before calculating the acceleration. The following is an example for a two-dimensional style problem:
- Example problem: April is pulling a 400 kg container to the left with a force of 150 Newtons. Bob stands on the left side of the container and pushes with a force of 200 Newtons. The wind is blowing to the left with a force of 10 Newtons. What is the acceleration of the container?
- Answer: the questions above provide complex clues to trick you. Draw a diagram and you will see a force of 150 Newtons to the right, 200 Newtons to the left, and 10 Newtons to the left. If "left" is positive, the resultant force on the object is 150 + 200 - 10 = 340 Newtons. Acceleration of object = F / m = 340 Newton / 400 kg = 0.85 m/s2.
