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1 year ago

prove displacement of a body in nth second is given by the S=u+a/2(2n-1) where symbols have their usual meaning

1 answer:

7 0

The proof that the displacement of a body in nth second which is given by the S=u+a/2(2n-1) is explained below.

<h3>Calculations and Parameters</h3>

Given:

u= initial velocity
a= acceleration

Displacement during nth second= displacement in n seconds- displacement in (n-1) seconds

= [ $un + \frac{1}{2} gn^2] - [ u(n-1) + \frac{1}{2} g(n-1)^2]$

= (u * 1) + g(n *1) - $\frac{g}{2}$ (1 *1)

Hence, in (n-1) seconds, n has a unit of time and 1 has a unit of time (not a constant)

Therefore, u(m/s) is multiplied by 1 (unit of time)

g(m/s^2) is multiplied by ( n*1 ), having units of time, i.e s^2

g/2 is also multiplied by ( 1 * 1, also having units of time, i.e s^2

Therefore, the equation is dimensionally correct and we should note that 1 is not a constant in the equation as the time of 1 second in (n-1) second.

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According to the graph, how many atoms would remain after two half-lives?

Fudgin [204]

Answer:

Let No be initial no of atoms

N = N0 / 2 after 1 half-life

N = N0 / 4 after 2 half-lives

So after 2 half-lives 20 of the 80 atoms remain

4 0

3 years ago

An electron moves with a speed of 8.0×106m/s along the -z-axis. It enters a region where there is a uniform magnetic field B = (

Crazy boy [7]

Answer:

Acceleration, $a=9.36\times 10^{18}\ m/s^2$

Explanation:

It is given that,

Speed of electron, $v=8\times 10^6\ m/s$

Charge on an electron, $q=1.6\times 10^{-19}\ C$

Mass of electron, $m=9.1\times 10^{-31}\ kg$

Magnetic field, $B=5.5i-3.7j$

Magnitude, $|B|=\sqrt{5.5^2+(-3.77)^2}=6.66\ T$

Magnetic force is given by :

$F=qvB$

Also, F = ma

$a=\dfrac{qvB}{m}$

$a=\dfrac{1.6\times 10^{-19}\times 8\times 10^6\times 6.66}{9.1\times 10^{-31}}$

$a=9.36\times 10^{18}\ m/s^2$

So, the acceleration of the electron is $9.36\times 10^{18}\ m/s^2$ . Hence, this is the required solution.

5 0

3 years ago

What do work and energy have in common

spayn [35]

Energy and Work have the same unit of measurement which is Joules in SI units.

Explanation:

A Joule of Work is said to be done on an object when energy is transferred to that particular object.
If two objects are involved, when one object transfers energy onto the second, a joule of work is said to be done by the first object.
Work is also the application of force on an object over a distance. So Work = Force × Displacement
Energy is neither created nor destroyed. It is in 2 forms - kinetic and potential.
Kinetic energy is defined as the energy of a moving object while potential energy is known as the energy that is stored within an object.
Kinetic Energy = 1/2 × mass × (velocity)²
Potential Energy = mass × acceleration due to gravity × height
Both energy and work are measured in Joules.