What causes an object's acceleration to increase or decrease?

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An object can slow down while experiencing an increase in acceleration if the velocity and acceleration are in opposite directions. Conversely, an object can speed up while its acceleration decreases if the acceleration is still in the same direction as the velocity but becoming less intense. For example, when driving, a driver may initially accelerate quickly and then gradually reduce the acceleration as they approach a desired speed. Similarly, during braking, a driver may start with light braking and then apply more force, resulting in increased acceleration while slowing down. The physics definition of acceleration is the change in velocity over time, expressed mathematically as acceleration equals velocity divided by time.
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Is it possible for an object to be slowing down while the magnitude of acceleration increasing? And is it possible for an object to be speeding up while its acceleration is decreasing?

I am a bit confused about the meaning of increasing and decreasing acceleration. I mean what makes an acceleration increase and decrease? Can someone give me an example please?
 
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Sure - all those things are possible. Keep in mind that "slowing down" or "speeding up" has to do only with the relative signs of the velocity and the acceleration - if they are opposite (say, velocity in the +x direction and acceleration in the -x direction), then the object will be slowing down, no matter whether the magnitude of the acceleration is constant or changing.

The simplest example might be what you do when you're driving your car. When you accelerate, you might push the accelerator pedal down to the floor at first, but then slowly let it come up as you get closer to your final speed - that's the magnitude of the acceleration decreasing as you speed up. Similarly, if you're braking, you might brake lightly at first, but then push hard on the brake pedal as you realize the guy in front of you just came to a stop - that's the magnitude of the acceleration increasing as you slow down.

Make sense?
 
Thanks for the great explanation! I was also having a hard time contemplating a situation. Also, what is the "physics" definition of acceleration? I've looked on webster's dictionary and websites of those nature but nothing that really define acceleration.
 
The physics definition is basically the change in velocity divided by the change over time.

Distance = x
Velocity = v
acceleration = a

v = x/t
a = v/t
 
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