Is Negative Acceleration Always Indicative of Slowing Down?

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SUMMARY

The discussion centers on the relationship between negative acceleration and the motion of an object, specifically addressing misconceptions about acceleration and velocity. It is established that acceleration can be zero at specific time intervals (0.5 min and 4.2 min) when the position function x(t) is constant. The participants confirm that negative acceleration indicates slowing down only when the velocity is positive, emphasizing that the signs of velocity and acceleration must be opposite for an object to decelerate. The conclusion is that only one statement regarding acceleration is true in the context provided.

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mncyapntsi
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Homework Statement
Which of the following statements are false:

The speed at 2.1 min is less than at 2.6 min.
The acceleration is zero at 0.5 min and 4.2 min.
The acceleration is non-zero at 6.2 min.
The acceleration is never negative.
The acceleration is non-zero at 2.3 min.

IMAGE BELOW
Relevant Equations
a(t) = dv/dt; v(t) = dx/dt; ...
I've written in that only the first statement was False, however my classmates aren't getting the same answer?
Please help clarify...

Screen Shot 2021-09-14 at 4.50.38 PM.png
 
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Can you explain why you think the rest are true?
 
PeroK said:
Can you explain why you think the rest are true?
Here is my reasoning:

The acceleration is zero at 0.5 min and 4.2 min: true because x(t)=constant so v(t)=0 so a(t)=0

i just rethought this one - false right?: The acceleration is non-zero at 6.2 min: false because x(t)=mx+p so v(t)=constant so a(t)=0

The acceleration is never negative: true bc nowhere is v(t)<0

i just rethought this one - false? The acceleration is non-zero at 2.3 min: false because x(t)=mx+p so v(t)=constant so a(t)=0
 
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mncyapntsi said:
The acceleration is never negative: true bc nowhere is v(t)<0
Negative acceleration means that the object is slowing down. Not that the velocity is negative.
 
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Right! So only one of them is true - the second one?
 
mncyapntsi said:
Right! So only one of them is true - the second one?
That's what I think.
 
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Thanks for helping me think through that, and clearing it up!:smile:
 
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PeroK said:
Negative acceleration means that the object is slowing down. Not that the velocity is negative.
Just to clarify, that is in the present context where the velocity is positive. More generally, slowing down means the velocity and acceleration have opposite sign.
 
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