Is Negative Acceleration Always Indicative of Slowing Down?

[mncyapntsi]

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...

 

[PeroK]

Can you explain why you think the rest are true?

 

[mncyapntsi]

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

 

[PeroK]

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.

 

[mncyapntsi]

Right! So only one of them is true - the second one?

 

[PeroK]

Right! So only one of them is true - the second one?

That's what I think.

 

[mncyapntsi]

Thanks for helping me think through that, and clearing it up!

 

[haruspex]

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.