Physics, 11.09.2019 23:20 ilovepickles930

The captain orders his starship to accelerate from rest at a rate of "1 g" (1 g = 9.8 m/s2). how many days does it take the starship to reach 5% the speed of light?
(light travels at 3.0 × 10^8 m/s.)

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Answer from: rosieposie27

17.7 days

Explanation:

Since the ship accelerates from the rest, its initial velocity would be equal to 0.

So,

$v_{i}=0$

Acceleration of the star-ship = a = 1 g = 9.8 m/s²

We need to find how many days will it take the ship to reach 5% of the speed of light. Speed of light is $3 \times 10^{8}$ m/s.

5% of the speed of light = $0.05 \times 3 \times 10^{8}=1.5\times 10^{7}$ m/s

This means, the final velocity of the star-ship will be:

$v_{f}=1.5\times 10^{7}$

We have the initial velocity, final velocity and the acceleration. We need to find the time(t). First equation of motion relates these quantities as:

$v_{f}=v_{i}+at$

Using the values in this equation, we get:

$1.5 \times 10^{7}=0+9.8(t)\\\\ t=\frac{1.5\times10^{7}}{9.8}\\\\ t=1,530,612.245$

Thus, the star-ship will take 1,530,612.245 seconds to reach to 5% the speed of light. Now we need to convert this time to days.

Since, there are 60 seconds in a minute:

1,530,612.245 seconds = $\frac{1,530,612.245}{60}=25510.20$ minutes

Since, there are 60 minutes in an hour:

25,510.20 minutes = $\frac{25,510.20}{60}=425.17$ hours

Since, there are 24 hours in a day:

425.17 hours = $\frac{425.17}{24}=17.7$ days

Thus, it will take approximately 17.7 days (approximately 17 days and 17 hours) to reach to 5% the speed of light

Answer from: Quest

an obstruction

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.

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