Speed vs Acceleration: Can An Object Do Both?

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Can an object be increasing in speed as its acceleration decreases? if so, give an example; if not explain why.
 
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As long as an object has positive acceleration, its speed will be increasing.

If an object is moving at, say 100 m/s, with acceleration, 10 m/s^2, as the acceleration decreases to 5 m/s^2, that is still a positive acceleration so its speed is still increasing.
 
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Yes. Like Hallofivy said above.

Think of being in a fast car getting onto the interstate from an on ramp. If you floor the accelerator, you will accelerate pretty quickly. Now, if you let off the accelerator a little bit, your acceleration slows down, but you are still increasing your velocity. Until the acceleration reaches zero or goes negative, then you will increase in speed.