The displacement of a particle on a vibrating string is given by the equations(t) = 9 +15sin(9πt)where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds.

Explanation:

Given the displacement of a particle expressed as

s(t) = 9 + 15sin(9πt) where s is measured incm and time in secs.

velocity is the change in displacement of the particle with respect to time:

v(t) = d(s(t))/dt

v(t) = 0+15(9π)cos(9πt)

v(t) = 135πcos(9πt)

Hence the velocity of the particle after t seconds is expressed as 135πcos(9πt)

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.

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.

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 . this process does not change the mass number.

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 -decay. in this the mass number remains same.

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