Physics, asked by sgoutamsharma, 5 months ago

drive the equation bof motion x = ut + ½at² vel​

Answers

Answered by MяƖиνιѕιвʟє
34

Correct Question :-

  • Drive the equation of motion s = ut + ½ at²

To prove :-

  • s = ut + ½ at²

Proof :-

As we know that

  • Average velocity = u + v/2

Where " u " is initial velocity and " v " is final velocity.

Distance travelled = Average velocity × time

→ s = (u + v)/2 × t

According to first equation of motion

→ v = u + at

So, put the value of " v "

→ s = (u + u + at)/2 × t

→ s = (2u + at)/2 × t

→ s = 2ut/2 + at²/2

→ s = ut + ½ at²

  • Hence proved
Answered by Intelligentcat
143

\Large{\boxed{\underline{\overline{\mathfrak{\star \: Correct Question :- \: \star}}}}}

Derive the second equation of motion :-

\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}

\red{\bigstar} Second equation of motion

\huge\leadsto{\sf\purple{Derive : }}

Let us consider, an object is moving along a straight line with a uniform acceleration (a) at t = 0 , initial velocity (u) . Let s be the distance travelled by the object in time t , from A to b.

↠ s = area enclosed by velocity time graph and time axis.

↠ s = Area of OABC

↠ s = Area of OACD + Area of ∆ ABD.

↠ s = OA × AD + 1/2 × BD × AD

↠ s = OA × OC + 1/2 (BC - CD) × OC. ...Eq(1)

OA = u

OC = t

BD = BC - CD = v - u.

↠ s = u × t + 1/2 (v - u) t

From first equation of motion we have , v - u = at.

↠ s = u × t × 1/2 × at × t

\therefore\underline{\boxed{\textsf{s = {\textbf{ut + 1/2at²}}}}} \qquad\qquad \bigg\lgroup\bold{2nd \ equation \ of \ motion} \bigg\rgroup

Hence ,

Derived !

Required information :-

You can derive first equation also in the same way .

First Equation of Motion

Let us consider an object is moving with uniform acceleration along a straight line . Let (u) be the initial velocity at t = 0 . After interval of time (t) , its velocity becomes u.

↠ Let OA = u [ t = 0 ]

Here in the figure we draw AD ⟂ BC , and BE ⟂ OY.

↠ ∠BAD = ϴ. [ say ]

Now,

↠ Acceleration = slope of Line AB

↠ a = tan ϴ

↠ a = BD/AD. [ tan ϴ = P/B ]

↠ a = (v - u)/t. [ AD = OC = t ]

\therefore\underline{\boxed{\textsf{v = {\textbf{u + at}}}}} \qquad\qquad \bigg\lgroup\bold{1st \ equation \ of \ motion} \bigg\rgroup

Or

\underline{\boxed{\textsf{at = {\textbf{v - u}}}}} \qquad\qquad \bigg\lgroup\bold{1st \ equation \ of \ motion} \bigg\rgroup

More related information :-

First equation of motion

❥ v = u + at.

v = final velocity.

u = initial velocity.

a = acceleration.

t = time taken.

Note :

first equation of motion also called velocity time equation.

✮ Second equation of motion

↠ s = ut + ½ at².

u = initial velocity.

a = acceleration.

t = time taken.

s = distance covered.

Note :-

Second equation of motion also called positive time equation.

✮ Third equation of motion

❥ v² - u² = 2as

v = final velocity.

u = initial velocity.

a = acceleration.

Note :-

Third equation of motion also called velocity positive equation.

First law of motion

↠ first law of motion states that an object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force.

Second law of motion

↠ second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.

Third law of motion

↠ third law of motion states that for every action there is an equal and opposite reaction and they act on two different bodies.

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