Question

derieve second equation of motion using graph ​

Answer 1

✯✯ QUESTION ✯✯

Derive second equation of motion using graph..

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✰✰ ANSWER ✰✰

Lets us consider a velocity time graph of Uniform acceleration a. Let point a represents initial velovity u. The velocity of the body is increased and point B represents Final Velocity v. E is the point on velovity axis representing v. C is the point on time axis representing time t. AD is perpendicular to BC.

For v= u + at

We know that slope of velovity gives acceleration.

$⇢a=Slope=\dfrac{BD}{AD}=\dfrac{CB-CD}{OC}$

$⇢\dfrac{OE-OA}{OC}$ (From Graph)

$⇢a=\dfrac{v-u}{t}$ --------- (i)

$⇢v-u=at$

☛$\large{\boxed{\bold{\bold{\purple{\sf{v=u+at}}}}}}$

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For $s=ut+\dfrac{1}{2}{at}^{2}$

We know that area under velovity time graph gives displacement..

S=area of OABC =area of Rec. OADC + Area of ΔBAD.

$⇢OA×OC+\dfrac{1}{2}×AD×BD$

$⇢s=ut+\dfrac{1}{2}OC×(BC-CD)$

$⇢s=ut+\dfrac{1}{2}t (v-u)$

☛$\large{\boxed{\bold{\bold{\red{\sf{s=ut+\dfrac{1}{2}{at}^{2}}}}}}}$

Answer 2

Answer:

s=UT+1/2at²

Explanation:

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