How to Calculate Acceleration

Calculating Acceleration from a Force

Define Newton’s Second Law of Motion. Newton’s second law of motion states that when the forces acting on an object are unbalanced, the object will accelerate. This acceleration is dependent upon the net forces that act upon the object and the object’s mass. Using this law, acceleration can be calculated when a known force is acting on an object of known mass. Newton’s law can be represented by the equation Fnet = m x a, where Fnet is the total force acting on the object, m is the object’s mass, and a is the acceleration of the object. When using this equation, keep your units in the metric system. Use kilograms (kg) for mass, newtons (N) for force, and meters per second squared (m/s) for acceleration.

Find the mass of your object. To find the mass of an object, simply place it on a balance or scale and find its mass in grams. If you have a very large object, you may need to find a reference that can provide you with the mass. Larger objects will likely have a mass with the unit of kilograms (kg). For this equation, you will want to convert the mass into kilograms. If the mass you have is in grams simply divide that mass by 1000 to convert to kilograms.

Calculate the net force acting on your object. A net force is an unbalanced force. If you have two forces opposing each other and one is larger than the other, you will have a net force in the direction of the larger force. Acceleration happens when an unbalanced force acts on an object, causing it to change speeds towards the direction the force is pushing or pulling it. For example: Let’s say you and your big brother 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 net force on the rope is 2 newtons to the right, in the direction of your brother. In order to properly understand the units, know that 1 newton (N) is equal to 1 kilogram X meter/second squared (kg X m/s).

Rearrange the equation F = ma to solve for acceleration. You can change this formula around to solve for acceleration by dividing both sides by the mass, so: a = F/m. To find the acceleration, simply divide the force by the mass of the object being accelerated. Force is directly proportional to the acceleration, meaning that a greater force will lead to a greater acceleration. Mass is inversely proportional to acceleration, meaning that with a greater mass, the acceleration will decrease.

Use the formula to solve for acceleration. Acceleration is equal to the net force acting on an object divided by the mass of the object. Once you’ve established the values for your variables, do the simple division to find the acceleration of the object. For example: A 10 Newton force acts uniformly on a mass of 2 kilograms. What is the object’s acceleration? a = F/m = 10/2 = 5 m/s

Calculating Average Acceleration from Two Velocities

Define the equation for average acceleration. You can calculate the average acceleration of an object over a period of time based on its velocity (its speed traveling in a specific direction), before and after that time. To do this you need to know equation for acceleration: a = Δv / Δt where a is acceleration, Δv is the change in velocity, and Δt is the amount of time it took for that change to occur. The unit for acceleration is meters per second per second or m/s. Acceleration is a vector quantity, meaning it has both a magnitude and a direction. The magnitude is the total amount of acceleration whereas the direction is the way in which the object is moving. If it is slowing down the acceleration will be negative.

Understand the variables. You can further define Δv and Δt: Δv = vf - vi and Δt = tf - ti where vf is the final velocity, vi is the initial velocity, tf is the ending time, and ti is the starting time. Because acceleration has a direction, it is important to always subtract the initial velocity from the final velocity. If you reverse them, the direction of your acceleration will be incorrect. Unless otherwise stated in the problem, the starting time is usually 0 seconds.

Use the formula to find acceleration. First write down your equation and all of the given variables. The equation is a = Δv / Δt = (vf - vi)/(tf - ti). Subtract the initial velocity from the final velocity, then divide the result by the time interval. The final result is your average acceleration over that time. If the final velocity is less than the initial velocity, acceleration will turn out to be a negative quantity or the rate at which an object slows down. Example 1: A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. What is its average acceleration? Write the equation: a = Δv / Δt = (vf - vi)/(tf - ti) Define the variables: vf = 46.1 m/s, vi = 18.5 m/s, tf = 2.47 s, ti = 0 s. Solve: a = (46.1 – 18.5)/2.47 = 11.17 meters/second. Example 2: A biker traveling at 22.4 m/s comes to halt in 2.55 s after applying brakes. Find his deceleration. Write the equation: a = Δv / Δt = (vf - vi)/(tf - ti) Define the variables: vf = 0 m/s, vi = 22.4 m/s, tf = 2.55 s, ti = 0 s. Solve: a = (0 – 22.4)/2.55 = -8.78 meters/second.

Confirming Your Understanding

Understand the Direction of Acceleration. The physics concept of acceleration doesn't always match how we would use the term in everyday life. Every acceleration has a direction, usually represented as positive if it's UP or RIGHT, and negative if DOWN or LEFT. See if your answer makes sense based on this breakdown: Behavior of a Car How is Velocity Changing? Direction of Acceleration Driver moving right (+) hits gas pedal + → ++ (more positive) positive Driver moving right (+) hits brakes ++ → + (less positive) negative Driver moving left (-) hits gas pedal - → -- (more negative) negative Driver moving left (-) hits brakes -- → - (less negative) positive Driver moves at constant velocity remains the same acceleration is zero

Understand the Direction of Force. Remember, a force only causes acceleration in the direction of the force. Some problems may try to trick you with irrelevant values. Example Problem: A toy boat with mass 10kg is accelerating north at 2 m/s. A wind blowing due west exerts a force of 100 Newtons on the boat. What is the boat's new northward acceleration? Solution: Because the force is perpendicular to the direction of motion, it does not have an effect on motion in that direction. The boat continues to accelerate north at 2 m/s.

Understand Net Force. If more than one force acts on an object, combine them into a net force before you calculate acceleration. For a problem in two dimensions, this looks something like this: Example Problem: April is pulling a 400 kg container right with a force of 150 newtons. Bob stand on the left of the container and pushes with a force of 200 newtons. A wind blowing left exerts a force of 10 newtons. What is the acceleration of the container? Solution: This problem uses tricky language to try and catch you. Draw a diagram and you'll see the forces are 150 newtons right, 200 newtons right, and 10 newtons left. If "right" is the positive direction, the net force is 150 + 200 - 10 = 340 newtons. Acceleration = F / m = 340 newtons / 400 kg = 0.85 m/s.

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