Physics q: Free fall

[AG22]

Hey everyone,

 

A question describes how two balls of different materials are dropped from a height and air resistance is neglible. If an object falls a distance of delta x during the first t seconds, how far does it fall during the first 3t seconds?

 

I realised that the object is uniformly accelarating (i.e. gravity) Soo, i used this equation: delta x = (v avg)(delta t) [because when there is a uniform acceleration, v avg = (v1+v2)/2]

That means that the object will fall 3 times delta x. Right? since x is proportional to t?

 

The solutions use the formula delta x = v1t +1/2at^2 And since v1 = 0, delta x is proportional to t^2. SO the real answer is the object will fall 9 times delta x in the first 3t seconds.

 

Can any one explain to me why I can't use this equation delta x = (v avg)(delta t) and hence cannot use the fact that x is proportional to t to give me the right answer? (even when it is uniformly accelerating?)

 

It would be greatly appreciated!

[Jochi1543]

 

The solutions use the formula delta x = v1t +1/2at^2 And since v1 = 0, delta x is proportional to t^2. SO the real answer is the object will fall 9 times delta x in the first 3t seconds.

 

Can any one explain to me why I can't use this equation delta x = (v avg)(delta t) and hence cannot use the fact that x is proportional to t to give me the right answer? (even when it is uniformly accelerating?)

 

I suck at explaining physics, but let me just tell you how I'd solve it and maybe it'll help.

 

You know:

V0 (zero for free fall)

a (which is g)

t

DeltaX1

 

 

Given these variables, your go-to formula will be theirs. Why? Because you don't have to calculate anything for it (whereas for your formula, you need to calculate V2). Always take the easiest route.

 

So, DeltaX1 = V0t + (g(t)^2/2). Since V0 = 0, it boils down to DeltaX1 = g(t)^2/2.

 

 

DeltaX2 = V0(3t) + (g(3t)^2)/2). Again, V0 = 0, so we get DeltaX2 = g(3t)^2/2. The trick here is that (3t)^2 = 9t^2.

 

Therefore, if we divide DeltaX2 by DeltaX1, we get 9. So in the time 3t, the object will travel a distance 9x farther than in the time t.

[switcheroo]

Jochi explains this well. I also wanted to point out that your (OP's) answer is intuitively wrong, possibly because I think you're confusing the effects of uniform acceleration and uniform velocity. In any case, recognizing intuitively wrong answers will become important for some questions on the real MCAT.

 

Think about it this way: If the object is moving at a uniform velocity (i.e., no acceleration), then the distance it moves should be proportional to time. But since the object in this question is accelerating, its velocity is increasing with every passing second--therefore, it wouldn't make sense for the object's delta x to be proportional to time, since velocity is not constant over the period of time measured. From an intuitive stance, it makes sense that the object could not move a distance of 3x in a time of 3t, and instead must move >3x in time 3t. I hope that makes sense...

[AG22]

Thanks both of you! It makes sense! B/c I don't have v2 figured out, I'm better off using their equation. Thanks!!

[AdamP]

listen to switch, you wont need eqns really ever.

 

a = constant, so v will be linear, d will be exponential.

 

you'll be able to pick the right mcq just by understanding that

[HBP]

t^2, thats all you need to know

 

i dont think i actually "solved" anything in PS