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Calculating Deceleration: Definition, Formula & Examples

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  • 0:02 Deceleration Background
  • 0:50 Deceleration Challenge
  • 3:28 Some Practice
  • 5:22 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser
In this lesson, you will learn about deceleration, what it means, and how it is a specific special case of acceleration. You will learn about which equations can be used to calculate deceleration and how to identify deceleration from position-time and velocity-time graphs of motion.

Deceleration Background

Have you ever been in a car that suddenly slowed down? Maybe there was a deer in the road or a child's ball rolled into the street and the driver had to slam on the breaks. Anytime you're in a vehicle and you feel yourself moving forward relative to the vehicle, you are decelerating. Deceleration is a special case of acceleration whereby it only applies to objects slowing down. Acceleration is a vector, which means that it has to be reported as a magnitude with a direction. In cases of one-dimensional motion, negative and positive are used to indicate direction. A way to determine whether deceleration is a part of a scenario is to compare the sign on the velocity and on the acceleration. If the signs are different, the object is decelerating.

Deceleration Challenge

Let's say that we've been given a challenge to interpret a set of data. Acting like investigators, let's come up with a theory explaining the data in Table 1.

Table 1

Time (s) Position (m) Velocity (m/s)
0 0 30
0.6 17.262 24.12
1.2 33.048 18.24
1.8 47.358 12.36
2.4 60.192 6.48
3 71.55 0.6

We can tell this object is decelerating because, as time progresses, the velocity decreases. The kinematics equations containing acceleration are given in Table 2.

Table 2

Let's solve equation 3 for a. This equation is the mathematical definition of acceleration, which is a change in velocity divided by the time required by that change to occur. We're going to use two sets of data to determine if the deceleration is constant.

Two Data Sets

Both results give the same acceleration, which tells us the acceleration is constant. Also, notice that the acceleration is negative, while the velocities are positive. This means the object is decelerating and it might be due to gravity because the magnitude of the deceleration is 9.8 meters per second squared. Our great physics detective skills tells us this object has been thrown up at an initial velocity of 30 meters per second. Let's make some graphs of the data to back up our case.

Position vs. Time Graph

Our first graph will look at position versus time. Graph 1 is position versus time for the data in Table 1. A linear line through the data is included to show that this data set is not linear, which is further evidence that the object is accelerating. Notice also that the tangent lines to the curve get more shallow as time progresses.

Slope on a position versus time graph is velocity. Graph 2 shows the first tangent line, Segment 1, and the last tangent line, Segment 2.

Graph with Segments

Put side by side, we can see that Segment 2 has a smaller slope than Segment 1. This means the object is decelerating.

Now let's look at a graph depicting velocity versus time.

Velocity vs. Time Graph

Slope on velocity versus time is acceleration. If we plot the velocity data versus the time data, we get a straight line. We can see the velocity (y values) decreasing because at zero seconds it is 30 meters per second, and three seconds later it is almost zero. We will pick two points along the line to prepare to calculate the slope of the line. Using these points, we will calculate the slope.

Graph with Slope Equations

Bingo! The acceleration is -9.8 meters per seconds squared. Did you notice that this is the same thing we calculated in our initial calculation? Our theory that a mass was launched straight up with an initial velocity of 30 meters per second is valid. Let's look at a few graphs to solidify our knowledge on deceleration.

Some Practice

Example 1

Prompt: Which curves or lines represent a deceleration?

Example 1

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