Conceptual Physics Questions

[dighn]

Originally posted by: Chaotic42
So if the function for velocity is v=2x²-8, v=0 when x=2. Since acceleration is the derivative of velocity, and v'=4x and x=2....

When v=0, v'=8.

Is that right?

looks right

 

[Chaotic42]

Originally posted by: dighn
looks right

Cool. Now I'm going to go prove that white is black. I just need to watch out for zebras. 😛

 

[dighn]

Originally posted by: Chaotic42

Originally posted by: dighn
looks right

Cool. Now I'm going to go prove that white is black. I just need to watch out for zebras. 😛

zebras are cool

 

[silverpig]

Originally posted by: Chaotic42
Let me venture into shaky territory (for me anyway). Note, I've never taken a physics class.

Someone said that acceleration must be 0 when velocity is 0.

So if the function for velocity is v=2x²-8, v=0 when x=2. Since acceleration is the derivative of velocity, and v'=4x and x=2....

When v=0, v'=8.

Is that right?

Yep you're right.

 

[silverpig]

Originally posted by: LordSnailz

Originally posted by: MrPickins

Originally posted by: LordSnailz

Originally posted by: MindStorm
You can get acceleration by taking the derivative of velocity. So how can acceleration be a non-zero number when velocity is 0? It can't. You can be accelerating when velocity is constant (i.e. rounding a curve at a constant 15 mph) but you have to have velocity to accelerate.

I concur, anyone with an answer?

Acceleration is a change in velocity.

Think of it this way: accel= (beginning velocity - end velocity)/ time...

If an object has a negative beginning velocity, but you accelerate it in the opposite direction until the end velocity is positive, you at some time (for just an instant) pass the point of zero velocity when the object changes direction.

The object hasn't finished changing velocity yet, thus it still has acceleration.

Originally posted by: Haircut :
...gravity does not stop acting on the ball when its velocity is zero.
As notfred said earlier no stopped object could ever start moving if acceleration is zero when velocity is zero.

but accel = (beginning velocity - end velocity)/ time, it's the derivative of delta_v(t)/t, so if v(t)=0, how can accel no be equal to zero?

...gravity does not stop acting on the ball when its velocity is zero.

true, but when we talk about accel, we're talking about whether or not the ball accelerates if velocity=0 ... there is not acceleration if the velocity is 0.

No accel if the velocity is 0? Think about that a second. If you slow something to v = 0, then by your definition, it can NEVER start moving again because you can't accelerate it.

derivitative of dv/dt... let v(t) = 2t
v(0) = 0
v'(t) = 2
v'(0) = 2

There's your 0 velocity and non-zero acceleration.


Also: speed != velocity
speed = v/||v|| (the magnitude of velocity)

If you go from A to B at 15 mph, then turn around and go from B to A at 15 mph, your average speed is 15 mph, but your average velocity is 0. (15 mph + (-15) mph)

 

[rgwalt]

First of all, velocity is a vector. Speed is a scalar. Velocity represents both rate of motion and direction of motion. So, when you have a change in direction that produces acceleration, while your speed hasn't changed, your direction has, hence you have a change in velocity.

Second, you can have a non-zero acceleration with a zero velocity.

a = dv/dt
*solve for dv and integrate*

v = vo + a*(t)

So when t = 0, v = vo. So, at t = 0, if vo = 0, you have a situation where you have zero velocity and non-zero acceleration.

Ryan