How to Find Average Acceleration: 10 Steps (with Pictures)

2024 Author: Jason Gerald | [email protected]. Last modified: 2024-01-19 22:11

Acceleration is a value that describes a change in speed, including a change in direction. You can find average acceleration to find the average velocity of an object over a period of time. Since this is not something people count on in everyday life, acceleration issues can be unusual. However, with the right approach you can understand these issues quickly.

Step

Part 1 of 2: Calculating Average Acceleration

Step 1. Understand what acceleration is

Acceleration describes how fast something is accelerating or slowing down. The concept is very simple indeed, even if your math textbook describes acceleration as "the change in velocity over time." Acceleration also describes where something is moving, which you can include as a written explanation or as part of a calculation:

• Usually, if an object is accelerating to the right, up, or forward, people write down the acceleration as a positive (+) number.
• If an object is accelerating left, down, or backward, use a negative number (-) to write the acceleration.

Step 2. Write down the definition of acceleration as a formula

As explained above, acceleration is change in speed over a period of time. There are two ways to write the acceleration formula:

• a_av = ^v/_t (The symbol or "delta" means "change.")
• a_av = ^{(v_f - v_i)}/_{(tf - ti)} In this equation, v_f is the final velocity, and v_i is the initial velocity.

Step 3. Find the initial and final velocities of an object

For example, if a car parked on the side of the road starts moving at 500 m/s to the right, its initial speed is 0 m/s, and its final speed is 500 m/s to the right.

• From now on, we will use positive numbers to describe the movement to the right, so we don't need to set the direction each time.
• If the car starts moving forward but ends up moving backwards, be sure to write the final speed in a negative number.

Step 4. Record the time change

For example, a car may take 10 seconds to reach its final speed. There are exceptions when the question says something different, this usually means t_f = 10 seconds and t_i = 0 seconds.

Make sure your speed and time are written in consistent units. For example, if your speed is written in miles per hour, the time should be written in hours as well

Step 5. Use these numbers to calculate the average acceleration

In our example:

• a_av = ^{(500 m/s - 0 m/s)}/_{(10s - 0s)}
• a_av = ^(500m/s)/_(10s)
• a_av = 50 m/s/s This can also be written as 50 m/s².

Step 6. Understand the results

Average acceleration describes how fast the speed changes over the time we're testing, on average. In the example above, the car is moving to the right, and every second the car is accelerating by an average of 50 m/s. Note that the details of a move may change, as long as the car stops with the same total change in speed and change in time:

• The car can start at 0 m/s and accelerate at a constant rate for 10 seconds, until the car reaches 500 m/s.
• The car can start at 0 m/s, accelerate to 900 m/s, then slow down to 500 m/s at 10 seconds.
• The car can start at 0 m/s, stay still for 9 seconds, then jump to a speed of 500 m/s very quickly at the tenth second.

Part 2 of 2: Understanding Positive and Negative Acceleration

Step 1. Know what positive and negative velocity represent

While speed always dictates direction, it can become tedious to keep writing "up" or "north" or "towards the wall." However, most math problems will assume that objects move along straight lines. Moving in one direction on a line is described as positive velocity (+), movement in the opposite direction is negative velocity (-).

For example, a blue train is moving east at 500 m/s. The red train is moving west just as fast, but because the red train is moving in the opposite direction from the blue train, the red train is moving at -500 m/s

Step 2. Use the meaning of acceleration to determine the + or - sign

Acceleration is the change in velocity over time. If you're confused about whether to write positive or negative acceleration, take a look at the change in velocity and see the results.:

v_end - v_beginning = + or - ?

Step 3. Understand the meaning of accelerating in each direction

Suppose a blue train and a red train are moving in opposite directions at a speed of 5 m/s. We can depict this on a number line, with the blue train moving at +5 m/s along the positive side of the number line, and the red train moving at -5 m/s along the negative side. If each train starts accelerating until the train is 2 m/s faster in the direction the train is moving, does each train have a positive or negative acceleration? Let's see:

• The blue train is moving faster along the positive side, so the speed of the blue train increases from +5 m/s to +7 m/s. The final velocity minus the initial velocity is 7 - 5 = +2. Since the change in velocity is positive, the acceleration is also positive.
• The red train is moving faster along the negative side, so the train starts at -5 m/s but ends up being -7 m/2. The final velocity minus the initial velocity is -7 - (-5) = -7 + 5 = -2 m/s. Since the change in velocity is negative, so is the acceleration.

Step 4. Understand what it means to slow down

Suppose an airplane starts moving at 500 miles per hour, then slows down to 400 miles per hour. Even though the plane is still moving in a positive or forward direction, the acceleration of the plane is negative, because the plane is moving more slowly forward than before. You can check in the same way as the example above: 400 - 500 = -100, so the acceleration is negative.

Meanwhile, if the helicopter is moving at -100 miles per hour and accelerating to -50 miles per hour, the helicopter is experiencing positive acceleration. This is because the change in velocity occurs in a positive direction: -50 - (-100) = +50, although the change is not sufficient to reverse the direction of the helicopter