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# Motion Equations Assignment Help

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Classical Physics - Motion Equations

**Motion Equations**

**(a) V = u + at; (b) s = ut + 1/2 at**^{2}

(c) v^{2 }– u^{2} = 2as; (d) snth = u + a/2 (2n – 1)

**Derivations**

**(a) A = dv/dt or dv = a dt**

∫vu dv = ∫to adt

V – u = at or v = u + at

(b) V = ds/ dt or ds = v .dt = ( u + at) dt

∫so ds = ∫to (u + at) dt

S = ut + at^{2} / 2

**(c) **Eliminate t from equations (I) and (2)

**T= v –u / a or s = u (v – u / a) + a/ 2 (v – u / a)**^{2}

Or v^{2 }– u^{2} = 2as

(d) Sn = un + a / 2 n^{2}

**Sn-1 = u (n – 1) = a/ 2 (n – 1)**^{2}

Sn^{th} = (Sn – Sn -1) = u + a/2 (2n – 1)

The conditions under which these equations can be applied

**(a) **Motion should be one dimensional

(b) Acceleration should be uniform

**(c) **Frame of reference should be inertial

Procedure to draw graphs

Consider the equation **v = u + at**

Compare the above equation with **y = c + ms,**

If **v** is along** y-axis, t **along **x axis**, then it is an equation of a straight line.

**If c - 0, that is, y = mx or v = at (u = 0)**

Then it is the equation of a straight line passing through origin.

Consider** s = ut + 1/2 at**^{2}

Compare the above equation with **y = ax + bx**^{2}. If s is (taken along **y – axis t** taken along **x – axis**) which is the general equation of a parabola.

Now even if **a = 0, that is, y = bx**^{2} or s = i/2 at^{2}

It is still the equation of a parabola. However if acceleration is zero that is, **b = 0** in general equation then**y = ax** or **s = ut** which is the equation of a straight line (passing through origin)

While drawing the curves these equations are to be kept in mind and accordingly the graph is drawn.

The other important equations are

**x**^{2} + y^{2} = a^{2} (equation of circle)

x^{2}/a^{2} + y^{2}/b^{2} = 1 (equation of an ellipse)

x2/a2 – y2/b2 = 1 (equation of hyperbola)

xy = c^{2} -> (equation of hyperbola)

Y = e-ax (exponential)

For example, radioactive disintegration or discharging of a capacitor and so on.

**Y = y**_{0}e^{-bx}

ExpertsMind.com - Physics Assignment Help, Motion Equations Assignment Help, Motion Equations Homework Help, Motion Equations Assignment Tutors, Motion Equations Solutions, Motion Equations Answers, Classical Physics Assignment Tutors

**Motion Equations**

**(a) V = u + at; (b) s = ut + 1/2 at**

(c) v

^{2}(c) v

^{2 }– u^{2}= 2as; (d) snth = u + a/2 (2n – 1)**Derivations**

**(a) A = dv/dt or dv = a dt**

∫vu dv = ∫to adt

V – u = at or v = u + at

(b) V = ds/ dt or ds = v .dt = ( u + at) dt

∫so ds = ∫to (u + at) dt

S = ut + at

∫vu dv = ∫to adt

V – u = at or v = u + at

(b) V = ds/ dt or ds = v .dt = ( u + at) dt

∫so ds = ∫to (u + at) dt

S = ut + at

^{2}/ 2**(c)**Eliminate t from equations (I) and (2)

**T= v –u / a or s = u (v – u / a) + a/ 2 (v – u / a)**

Or v

(d) Sn = un + a / 2 n

^{2}Or v

^{2 }– u^{2}= 2as(d) Sn = un + a / 2 n

^{2}

**Sn-1 = u (n – 1) = a/ 2 (n – 1)**

Sn

^{2}Sn

^{th}= (Sn – Sn -1) = u + a/2 (2n – 1)The conditions under which these equations can be applied

**(a)**Motion should be one dimensional

**Acceleration should be uniform**

(b)

(b)

**(c)**Frame of reference should be inertial

Procedure to draw graphs

Consider the equation

**v = u + at**

Compare the above equation with

**y = c + ms,**

If

**v**is along

**y-axis, t**along

**x axis**, then it is an equation of a straight line.

**If c - 0, that is, y = mx or v = at (u = 0)**

Then it is the equation of a straight line passing through origin.

Consider

**s = ut + 1/2 at**

^{2}

Compare the above equation with

**y = ax + bx**

^{2}. If s is (taken along

**y – axis t**taken along

**x – axis**) which is the general equation of a parabola.

Now even if

**a = 0, that is, y = bx**

^{2}or s = i/2 at^{2}

It is still the equation of a parabola. However if acceleration is zero that is,

**b = 0**in general equation then

**y = ax**or

**s = ut**which is the equation of a straight line (passing through origin)

While drawing the curves these equations are to be kept in mind and accordingly the graph is drawn.

The other important equations are

**x**

x

x2/a2 – y2/b2 = 1 (equation of hyperbola)

xy = c

Y = e-ax (exponential)

^{2}+ y^{2}= a^{2}(equation of circle)x

^{2}/a^{2}+ y^{2}/b^{2}= 1 (equation of an ellipse)x2/a2 – y2/b2 = 1 (equation of hyperbola)

xy = c

^{2}-> (equation of hyperbola)Y = e-ax (exponential)

For example, radioactive disintegration or discharging of a capacitor and so on.

**Y = y**

_{0}e^{-bx}

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