Positive Acceleration: Is Slowing Down in Negative Direction Considered?

[cvc121]

Hi,

I was always told that positive acceleration means that an object is always speeding up. However, I am starting to question this. I know that if an object is speeding up in the positive direction, the acceleration is positive. However, if an object is slowing down in the negative direction, the calculated acceleration will be positive, even though the object is slowing down. If an object is slowing down in the negative direction, is this considered positive acceleration.?

For example, in the graph below (please ignore the area calculations), the object experiences positive acceleration during 0-2s and 10-12s. Is the object also experiencing positive acceleration during 8-10s?

Thanks! All help is very much appreciated!

 

[Doc Al]

For example, in the graph below (please ignore the area calculations), the object experiences positive acceleration during 0-2s and 10-12s. Is the object also experiencing positive acceleration during 8-10s?

Sure. You can easily determine the sign of the acceleration by looking at the slope of the velocity-time graph. After all, acceleration = Δv/Δt.

 

[CWatters]

Consider the point t=10s. The acceleration is positive (Positive slope) however just before t=10 the velocity is negative and slows to zero at t=10. After t=10 the velocity is positive and increasing. So the speed can be either Increasing, decreasing or zero when you have positive acceleration.

 

[Chandra Prayaga]

We should not get fixated on the signs, which depend on the choice of coordinate system The correct statements, independent of how you draw your coordinate system, are: (1) If the velocity and acceleration are in the same direction, the speed increases. (2) If they are in opposite directions, the speed decreases. (3) If the acceleration is perpendicular to the velocity, the velocity changes direction without change in speed.

 

[nasu]

You can consider that usually the positive direction is chosen as the direction of the motion (or direction of velocity). If this is the case, a positive acceleration will correspond to speeding up and negative acceleration to slowing down. Some intro textbooks may keep this convention and so they will tell this "rule".
But it is not a general statement, as you were already told.

 

[mathman]

The main thing to understand is that acceleration and velocity are vectors, which means they have a magnitude and a direction, so for both quantities it is better to look at the direction in 3-space rather than positive or negative, which assumes a one dimensional situation.