Question

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Answer 1

$Solution:-</p><p></p><p>To prove :-</p><p></p><p>\huge 2as = v^2 - u^22as=v2−u2</p><p></p><p>By calculus method.</p><p></p><p>Proof :-</p><p></p><p>Let a body moves with constant acceleration a by initial velocity u and after time t it's final velocity becomes v.</p><p></p><p>then,</p><p></p><p>→\huge \vec{a} = \dfrac{dv}{dt}a=dtdv</p><p></p><p>→\huge a = \dfrac{dv}{ds} \times \dfrac{ds}{dt}a=dsdv×dtds</p><p></p><p>→\huge a = \dfrac{dv}{ds}\times dva=dsdv×dv</p><p></p><p>→\huge \int_{u}^{v}v.dv∫uvv.dv \huge = \int_{0}^{s}ads=∫0sads</p><p></p><p>→\huge [v]_u^v = a [s]_0^s[v]uv=a[s]0s</p><p></p><p>→\huge [\dfrac{v^2}{2}]_u^v = a [s]_0^s[2v2]uv=a[s]0s</p><p></p><p>→\huge \dfrac{v^2 - u^2}{2}= as2v2−u2=as</p><p></p><p>→\huge v^2 - u^2 = 2asv2−u2=2as proved..</p><p></p><p>Parallax method :-</p><p></p><p>The method which is used to measure the large distances such as distance between sun and earth moon and earth etc is called parallax method.</p><p></p><p>When we see an object from both eyes the position of the object fluctuates when seen from one eye it is due to the parallax.</p><p></p><p>The direction along which an object is viewed subtended an angle between the two lines known as parallax angle.</p><p></p><p>For measuring the distance by parallax method we use the formula :-</p><p></p><p>★ \huge \boxed{\sf{ r = \dfrac{l}{\theta}}}r=θl</p><p></p><p>where \thetaθ is the parallax angle.</p><p></p><p>, r is the distance between the point of observation to the object, and l is the distance between the point of observations.</p><p></p><p>$

Answer 2

$a = \frac{dv}{dt}$

$a = \frac{ds}{dt} . \frac{dv}{ds} = v \frac{dv}{ds}$

$v .\: dv = a. \: d s$

$\int _{u} ^{v} v \: dv = a\int_{s _{i}} ^{s _{f} } ds$

$( \frac{ {v}^{2} }{2} ) | _{u} ^{v} = a(s) | _{s _{i} } ^{s_{f}}$

${v}^{2} - {u}^{2} = 2a(s_f - s_i)$

If, The particle starts from origin , then initial displacement is 0

$\implies {v}^{2} - {u}^{2} = 2as$