Physics Test - how smart are you?

An object moves at the speed of 3x^2 + 4x - 3 where x is it's coordinate according to the trajectory (it's a straight line) if we assume that the object starts to move at x=0. What is the jerk of this motion?

Originally posted by kbaumen
An object moves at the speed of 3x^2 + 4x - 3 where x is it's coordinate according to the trajectory (it's a straight line) if we assume that the object starts to move at x=0. What is the jerk of this motion?

OK, there may be mistakes in this, but...

velocity = f(x)
acceleration = df/dt = f'u = f'f
jerk = da/dt = f''fu + f'^2u = (f''f + f'^2)f

Here f(x) = 3x^2 + 4x - 3
f'(x) = 6x + 4
f''(x) = 6

So in terms of x, this comes out as...
jerk = 2(3x^2 + 4x - 3)(27x^2 + 36x - 1)

Or, initially, = 6.

Originally posted by mtthw
OK, there may be mistakes in this, but...

velocity = f(x)
acceleration = df/dt = f'u = f'f
jerk = da/dt = f''fu + f'^2u = (f''f + f'^2)f

Here f(x) = 3x^2 + 4x - 3
f'(x) = 6x + 4
f''(x) = 6

So in terms of x, this comes out as...
jerk = 2(3x^2 + 4x - 3)(27x^2 + 36x - 1)

Or, initially, = 6.

Yep, correct. Jerk is the second derivative of velocity.

Originally posted by kbaumen
Yep, correct. Jerk is the second derivative of velocity.

I thought it was called "impulse".

EDIT: I stand corrected! http://en.wikipedia.org/wiki/Classical_mechanics

No, impulse = mass x velocity. The bigger is impulse, the bigger the impact will be if this object hits another one, thus the hit object will move at larger speed.

Imagine you throw a rock in a lake. The water surface starts oscillating, which emits a transversal wave that can be described by the equation s = 0.3 * cos * 2pi(t/0.25 - x/0.5). By knowing this, calculate:
a)amplitude
b)period
c)frequency

P.s. All values in the equation are given in SI system.

Originally posted by kbaumen
Imagine you throw a rock in a lake. The water surface starts oscillating, which emits a transversal wave that can be described by the equation s = 0.3 * cos * 2pi(t/0.25 - x/0.5). By knowing this, calculate:
a)amplitude
b)period
c)frequency

P.s. All values in the equation are given in SI system.

Do we by any chance get to know what X, T and S are? I can guess about T, time?, X=? S=? Distance ususally but here? With three variables you get T= (S/0.3cos (2*PI)+2X)/4
But that tells us nothing without pegging a # for X or S.
You can plug in an infinite set of numbers including negatives and irrationals and find an infinite set of conditions satisfying that equation.

That's the equation of harmonic oscillations (if I correctly translated).
s - the distance particles move away from their equilibrium position
t-time
x-distance from wave emitter in the direction of wave movement.
If the T would be capitalized, then it would be the wave's period - time needed for one full oscillation.

Pardon for my English, if that's hard to understand, just ask, I'll try to explain. I used a dictionary, so I'm not quite sure all these terms are used in physics.

P.S. You can rewrite the equation as s = A * cos * (w * t - k * x).
w (greek omega) - angular frequency, k - wave number calculated -> 2pi/lambda where lambda = wave length.

EDIT: This equation is used as a function if you want to analyze this wave graphically. If you draw it, you get a sinusoid. Though this is not required, you can get all the things asked from the equation, you just have to know what is what.

Is there really no-one to figure this out?

Originally posted by kbaumen
That's the equation of harmonic oscillations (if I correctly translated).
s - the distance particles move away from their equilibrium position
t-time
x-distance from wave emitter in the direction of wave movement.
If the T would be capitalized, then it would be the wave's period - time needed for one full oscillation.

Pardon for my English, if that's ...[text shortened]... ed, you can get all the things asked from the equation, you just have to know what is what.

Excuse me for my English but what Is written there is not harmonic oscillation equation. It is wave propagation equation. Anyway, all the values asked are easy to calculate from this equation.

Originally posted by kbaumen
Imagine you throw a rock in a lake. The water surface starts oscillating, which emits a transversal wave that can be described by the equation s = 0.3 * cos * 2pi(t/0.25 - x/0.5). By knowing this, calculate:
a)amplitude
b)period
c)frequency

P.s. All values in the equation are given in SI system.

OK:

(a) amplitude = 0.3
(b) period = 0.25
(c) frequency = 1/period = 4

all by inspection.

Originally posted by PBE6
OK:

(a) amplitude = 0.3
(b) period = 0.25
(c) frequency = 1/period = 4

all by inspection.

Yep, correct, wasn't that hard at all.

Hey, Ramned, do you have any more of those questions?

Originally posted by Ramned
[b]Harder!

1. When looking into a concave mirror, is the image you see
A) Virtual B) Real C) Possibly both, real or virtual.
2. True or False: Convex mirrors magnify the images.
3. What produces a higher pitch at the fundamental frequency, a closed pipe or an open pipe? Why?
4. When you see a longitudinal wave, what is the relati ...[text shortened]... ) questions I can think of! Appears that AThousandYoung has common sense / is a good physicist.[/b]

im not sure if anyone has answered 1 and 2...After a quick scan,it doesnt look like it. Sorry if they have already been answered

1. C. For Concave mirrors, the image is real when the object is at all points beyond F, and it is virtual when the object is between F and the mirror.

2. False. convex mirrors do not magnify images. Wherever the object is placed, the image will be virtual, erect, and smaller.

Originally posted by kbaumen
Yep, correct. Jerk is the second derivative of velocity.

You want to try my post, the maximum bug flow into a pool skimmer?
Nobody has taken it on yet.