How can acceleration be positive or negative

This indicates that your arrow is actually pointing in the wrong way. So getting a negative acceleration in these cases indicates some sort of frame of reference- that positive is going one way, and negative the other.

So, having a "negative" acceleration depends on the case you're dealing with, and it's not really something physical. It usually just results from conventional mathematical modelling.

How can acceleration be negative? Physics 1D Motion Acceleration. Jan 15, An object uniformly accelerates from What is the rate of What is its This discussion illustrates that a free-falling object that is accelerating at a constant rate will cover different distances in each consecutive second.

Further analysis of the first and last columns of the data above reveal that there is a square relationship between the total distance traveled and the time of travel for an object starting from rest and moving with a constant acceleration. The total distance traveled is directly proportional to the square of the time.

For objects with a constant acceleration, the distance of travel is directly proportional to the square of the time of travel. The average acceleration a of any object over a given interval of time t can be calculated using the equation.

This equation can be used to calculate the acceleration of the object whose motion is depicted by the velocity-time data table above. The calculation is shown below. Typical acceleration units include the following:. These units may seem a little awkward to a beginning physics student.

Yet they are very reasonable units when you begin to consider the definition and equation for acceleration.

The reason for the units becomes obvious upon examination of the acceleration equation. Since acceleration is a vector quantity , it has a direction associated with it. The direction of the acceleration vector depends on two things:. The general principle for determining the acceleation is:. This general principle can be applied to determine whether the sign of the acceleration of an object is positive or negative, right or left, up or down, etc.

Consider the two data tables below. In each case, the acceleration of the object is in the positive direction. In Example A, the object is moving in the positive direction i. When an object is speeding up, the acceleration is in the same direction as the velocity.

Thus, this object has a positive acceleration. In Example B, the object is moving in the negative direction i. According to our general principle , when an object is slowing down, the acceleration is in the opposite direction as the velocity. Thus, this object also has a positive acceleration. This same general principle can be applied to the motion of the objects represented in the two data tables below. Conversely, a positive acceleration means that the change in the velocity points in the positive direction.

Kinematics is the correct use of the parameters position, velocity, and acceleration to describe motion. Learning to use these three terms correctly can be made much easier by learning a few tricks of the trade.

These tricks, or analysis tools, are detailed in the following section. The words used by physicists to describe the motion of objects are defined above. However learning to use these terms correctly is more difficult than simply memorizing definitions. A motion diagram can be thought of as a multiple-exposure photograph of the physical situation, with the image of the object displayed at equal time intervals. For example, a multiple-exposure photograph of the situation described above would look something like this:.

Note that the images of the automobile are getting closer together near the end of its motion because the car is traveling a smaller distance between the equally-timed exposures.

In general, in drawing motion diagrams it is better to represent the object as simply a dot, unless the actual shape of the object conveys some interesting information.

Thus, a better motion diagram would be:. Remember, to define a coordinate system you must choose a zero, define a positive direction, and select a scale. We will always use meters as our position scale in this course, so you must only select a zero and a positive direction. Remember, there is no correct answer. Any coordinate system is as correct as any other. The choice below indicates that the initial position of the car is the origin, and positions to the right of that are positive.

We can now describe the position of the car. The car starts at position zero and then has positive, increasing positions throughout the remainder of its motion. We can now describe the velocity of the car. Since the velocity vectors always point in the positive direction, the velocity is always positive. The car starts with a large, positive velocity which gradually declines until the velocity of the car is zero at the end of its motion.

Since acceleration is the change in velocity of the car during a corresponding time interval, and we are free to select the time interval as the time interval between exposures on our multiple-exposure photograph, we can determine the acceleration by comparing two successive velocities. The change in these velocity vectors will represent the acceleration. Thus, the acceleration points to the left and is therefore negative. You could construct the acceleration vector at every point in time, but hopefully you can see that as long as the velocity vectors continue to point toward the right and decrease in magnitude, the acceleration will remain negative.

Thus, with the help of a motion diagram, you can extract lots of information about the position, velocity, and acceleration of an object. You are well on your way to a complete kinematic description. The verbal representation of the situation has already been translated into a motion diagram. A careful reading of the motion diagram allows the construction of the motion graphs.

We already know, from the motion diagram, that the car starts at position zero, then has positive, increasing positions throughout the remainder of its motion. This information can be transferred onto a position vs. Notice that the position is zero when the time is equal to zero, the position is always positive, and the position increases as time increases.

Also note that in each subsequent second, the car changes its position by a smaller amount. This leads to the graph of position vs. Once the car stops, the position of the car should not change. From the motion diagram, we know that the velocity of the car is always positive, starts large in magnitude, and decreases until it is zero.

This information can be transferred onto a velocity vs. How do we know that the slope of the line is constant? The slope of the line represents the rate at which the velocity is changing, and the rate at which the velocity is changing is termed the acceleration. Since in this model of mechanics we will only consider particles undergoing constant acceleration, the slope of a line on a velocity vs. From the motion diagram, the acceleration of the car can be determined to be negative at every point.

Again, in this pass through mechanics we will only be investigating scenarios in which the acceleration is constant.

Thus, a correct acceleration vs. After constructing the two qualitative representations of the motion the motion diagram and the motion graphs , we are ready to tackle the quantitative aspects of the motion. A glance at the situation description should indicate that information is presented about the car at two distinct events. Information is available about the car at the instant the driver applies the brakes the velocity is given , and the instant the driver stops the position is given.

Other information can also be determined by referencing the motion diagram. To tabulate this information, you should construct a motion table. In addition to the information explicitly given, the velocity at the first event and the position at the second event, other information can be extracted from the problem statement and the motion diagram. Since you are working under the assumption in this model that the acceleration is constant, the acceleration between the two instants in time is some unknown, constant value.

To remind you that this assumption is in place, the acceleration is not labeled at the first instant, a1, or the second instant, a2, but rather as the acceleration between the two instants in time, a You now have a complete tabulation of all the information presented, both explicitly and implicitly, in the situation description. Moreover, you now can easily see that the only kinematic information not known about the situation is the assumed constant acceleration of the auto and the time at which it finally stops.

Thus, to complete a kinematic description of the situation these two quantities must be determined. What you may not know is that you have already been presented with the information needed to determine these two unknowns. In the concepts and principles portion of this unit, you were presented with two formal, mathematical relationships, the definitions of velocity and acceleration.

In the example that you are working on, there are two unknown kinematic quantities. You should remember from algebra that two equations are sufficient to calculate two unknowns.

Thus, by applying the two definitions you should be able to determine the acceleration of the car and the time at which it comes to rest. Although you can simply apply the two definitions directly, normally the two definitions are rewritten, after some algebraic re-arranging, into two different relationships. This rearrangement is simply to make the algebra involved in solving for the unknowns easier. It is by no means necessary to solve the problem. In fact, the two definitions can be written in a large number of different ways, although this does not mean that there are a large number of different formulas you must memorize in order to analyze kinematic situations.

There are only two independent kinematic relationships. The two kinematic relationships [1] we will use when the acceleration is constant are:. Thus, the car must have accelerated at 3. The kinematic description of the situation is complete. When she is 10 m from the light, and traveling at 8. She instantly steps on the gas and is back at her original speed as she passes under the light.

Notice that between the instant she hits the brakes and the instant she steps on the gas the acceleration is negative, while between the instant she steps on the gas and the instant she passes the light the acceleration is positive. Thus, in tabulating the motion information and applying the kinematic relations we will have to be careful not to confuse kinematic variables between these two intervals. Below is a tabulation of motion information using the coordinate system established in the motion diagram.

Recall that by using your two kinematic relations you should be able to determine these values. Second, notice that during the second time interval again two variables are unknown. Once again, the two kinematic relations will allow you to determine these values.