Physics, 22.02.2020 06:10 bitterswt01

A particle's velocity is given by the function Vx = (2.2 m/s) * sin (pi * t), where t is in seconds. What is the first time after t=0 s when the particle reaches a turning point?

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Answer from: middlegirlrule9453

After 1 seconds

Explanation:

The velocity of the particle is given by a periodic function, in the form

$v_x=(2.2) sin (\pi t)$ [m/s]

where

t is the time, in seconds

A periodic function is written in the form

$y=Asin(\omega t)$

where

A is the amplitude (maximum displacement from equilibrium position)

$\omega$ is the angular frequency, which can be written as

$\omega=\frac{2\pi}{T}$

where T is the period.

For the periodic function in this problem, we have

A = 2.2 m/s

$\omega= \pi$ [rad/s]

So the period is:

$T=\frac{2\pi}{\pi}=2 s$

The particle reaches a turning point when the velocity becomes zero, and then it becomes negative.

At t = 0, the function has value of zero.

After 1/4 of period, which corresponds to 0.5 seconds, the function reaches its maximum:

$v(0.5 s)=(2.2)\cdot sin(\pi \cdot 0.5)=2.2$

After 1/2 of period, which corresponds to 1 second, the function becomes zero again:

$v(1s)=2.2\cdot sin (\pi \cdot 1)=0$

Therefore, the particle reaches the first turning point at t = 1 sec.

Answer from: Quest

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

$_a^z\textrm{x}\rightarrow _{a-2}^{z-4}+_2^4\alpha$

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

$_a^z\textrm{x}+_{-1}^0\textrm{e}\rightarrow _{z-1}^a\textrm{y}$

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases $\gamma -radiations$ . this process does not change the mass number.

$_a^z\textrm{x}^*\rightarrow _a^z\textrm{x}+_0^0\gamma$

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as $\beta ^+$ -decay. in this the mass number remains same.

$_a^z\textrm{x}\rightarrow _{z-1}^a\textrm{y}+_{+1}^0e$

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

Answer from: Quest

Kinetic energy = 1/2mv^2. since the mass is constant we can form a ratio of it's kinetic energy at 60 divided by that at 30 to see ke(60)/ke(30) = +(60^2)/30^2). this may be said to 300% increase.

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A particle's velocity is given by the function Vx = (2.2 m/s) * sin (pi * t), where t is in seconds....

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