AAMC 4 PS section question

[folktale]

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After a block began to slide, how did its speed vary with time? (Note: Assume that the tension and kinetic friction forces on the block were constant in magnitude.)

A. It was constant in time
B. It increased exponentially with time
C. It was first constant, then increased linearly with time
D. It increased linearly with time

Answer: D

I thought it was B b/c as time progresses, I thought that the velocity exponentially increases due to gravity? And the kinetic friction shouldn't matter b/c it's constant.

 

[MedPR]

Constant acceleration means linear velocity increase. a=vf-vi/t

 

[folktale]

Oh I forgot to mention, that the block in question is on a board that has friction, connected to a mass hanging via a string. Once the mass is released, it accelerates down via gravity, causing the block to move across the board. So constant acceleration meaning gravitational acceleration. And using F=ma, since both the force and the acceleration is constant, it has to be linear? I am just confused because I've always thought that an object falling usually increase in velocity exponentially. Maybe this exponential thinking is only true for free fall?

 

[MedPR]

Oh I forgot to mention, that the block in question is on a board that has friction, connected to a mass hanging via a string. Once the mass is released, it accelerates down via gravity, causing the block to move across the board. So constant acceleration meaning gravitational acceleration. And using F=ma, since both the force and the acceleration is constant, it has to be linear? I am just confused because I've always thought that an object falling usually increase in velocity exponentially. Maybe this exponential thinking is only true for free fall?

Constant acceleration means linear velocity increase, always. Free fall is a case of constant acceleration, so the velocity increases linearly with time. The distanec it falls is exponential because the speed is increasing.

http://www.walter-fendt.de/ph14e/acceleration.htm

 

[folktale]

Thanks for clearing it up!

 

[HollowSuperet36]

acceleration down a slanted plane can be defined as:

@=Theta
Fk=Coefficient of kinetic friction

a=g(sin@-Fkcos@)

Thus, given that your block is moving at all as stated in the question it must be accelerating. And acceleration is fully dependent upon gravity.

Distance over time graph would start somewhat slow and turn rather steep.
(Due to the square function of time in x=1/2at^2)

Velocity over time graph would reveal a straight slanted line increasing steadiliy over time.

Acceleration would be a straight line with no slant.

This can also be witnessed in assessing the units of each

Distance= m
Velocity= m/s
Acceleration= m/s/s

 

[folktale]

Anyone have a list of exponential, inverse, and linear relationships?

 

[MedPR]

Anyone have a list of exponential, inverse, and linear relationships?

If there was, it would be pretty long. It's easiest to see the relationships by looking at the equations.

 

[HollowSuperet36]

Nvm,

Just realized MedPR posted a link to a pictorial already.

Does that not answer your question?

 

[MedPR]

^MedPR

Not really, you should be familiar with these relationships by the graphs used for rate laws.

See attached.

Based on the OP, he's probably looking for a list of how things are related, not what the graphs look like.

But yes, the graphs should be a familiar topic.

 

[folktale]

The link seems to be not showing the diagrams it's supposed to be showing.