berkeley review physics section 2 (force) question 5

[keikoblue2]

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Hello, the question asks:

"If the raindrop starts its fall from rest, which graph BEST represents the relation between the drop's instantaneous speed and time?"

The answer is B, the second picture. The explanation is: "... although [A] says that the drop starts from rest and eventually gets to terminal velocity, at v = Vt (terminal velocity), the speed abruptly stops changing. This does not happen. Most things in nature happen smoothly. is correct because it starts from rest and smoothly approaches Vt."

But for answer B, doesn't the acceleration change since the slope of the graph gets less steep as time increases? Doesn't this mean acceleration decreases (and I thought acceleration of gravity is constant at 9.8 near Earth's surface)? I chose answer A because the acceleration is constant (slope of graph is same for each time frame) and the velocity increases from 0 to terminal velocity.

I'm really confused 🙁 Help is appreciated!

 

[secretsunset29]

I'm not sure if my answer is "scientifically accurate", but here's my thinking: acceleration is constant, yes....but, instantaneous speed cannot be constant if acceleration is constant. Speed increases exponentially when acceleration is constant.

 

[Sterling Archer]

I haven't seen the related passage, but here's my take:
The slope of a velocity / time graph is the acceleration. Since terminal velocity is mentioned, I'm assuming that this is no longer an ideal situation. If terminal velocity is a factor, then acceleration of the raindrop is not constant. As the raindrop increases in its velocity, so does the drag force in the opposite direction. The force due to gravity is constant (mg), but the drag force increases gradually with the velocity, so the net force (and thus, net acceleration) gradually decreases as drag force becomes more equal to the force of gravity. Eventually, the net force (and thus, acceleration) becomes 0 at it's terminal velocity.

 

[keikoblue2]

I'm not sure if my answer is "scientifically accurate", but here's my thinking: acceleration is constant, yes....but, instantaneous speed cannot be constant if acceleration is constant. Speed increases exponentially when acceleration is constant.

Yeah, the instantaneous speed is increasing in both graphs above. But isn't when acceleration is constant, the slope of the velocity vs time graph is linear (straight slope), not exponential? B/c for constant acceleration, the velocity is increased by x m/s for each time frame. Ex: At time = 0, velocity is 0. At t = 1, V = 9.8 m/s. At t = 2, v = 19.6 m/s. At t = 3, v = 29.4 m/s, etc... If you plot this out, it's a linear graph, isn't it, since V is increasing by the same amount for each time increment? For a velocity vs time graph to be exponential, the acceleration would change over time.

I haven't seen the related passage, but here's my take:
The slope of a velocity / time graph is the acceleration. Since terminal velocity is mentioned, I'm assuming that this is no longer an ideal situation. If terminal velocity is a factor, then acceleration of the raindrop is not constant. As the raindrop increases in its velocity, so does the drag force in the opposite direction. The force due to gravity is constant (mg), but the drag force increases gradually with the velocity, so the net force (and thus, net acceleration) gradually decreases as drag force becomes more equal to the force of gravity. Eventually, the net force (and thus, acceleration) becomes 0 at it's terminal velocity.

The passage was unrelated to the question (except for the definition of terminal velocity) but your explanation makes perfect sense! I completely ignored drag force/net force and assumed gravity was the only force acting on the raindrop, stupid of me. Thanks so much, this was a much better explanation that what BR gave 🙂