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Acceleration is a fundamental concept in physics that quantifies the rate at which an object’s velocity changes over time. It plays a crucial role in understanding the dynamic behavior of moving objects and is therefore often calculated to analyze and predict their motion. Whether it is a car speeding up, a ball falling due to gravity, or a rocket launching into space, the ability to determine acceleration accurately and efficiently is essential. In this guide, we will explore the principles and methods behind calculating acceleration, providing you with a comprehensive understanding of this fundamental physical quantity.
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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
- 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.
- 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.
- 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
- 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.
- 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
- 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.
- 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.
- 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
| 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 |
- 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 .
- 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 .
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.
In conclusion, calculating acceleration is a fundamental concept in physics that allows us to understand an object’s change in velocity over time. By using the formula a = (v_f – v_i) / t, where a is acceleration, v_f is final velocity, v_i is initial velocity, and t is the time elapsed, we can accurately determine the rate at which an object is speeding up or slowing down. Furthermore, acceleration calculation is essential in numerous areas of study, such as mechanics, kinematics, and engineering, as it provides valuable insights into the motion and dynamic behavior of objects. Whether analyzing the motion of a car, an athlete, or a celestial body, understanding how to calculate acceleration is crucial for investigating and predicting various phenomena in the natural world.
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