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A person travels with initial velocity 10m/s, when it accelerates 15m/s² it goes to final velocity 20m/s. Find the displacement?​

Answer 1

Given:

• Initial velocity = u = 10m/s

• Final velocity = v = 20m/s

• acceleration = a = 15m/s²

To Find:

• Displacement

=> Using Equation of motion:

$</p><p></p><p>\mapsto \sf\boxed{\bold{\pink{v {}^{2} = u {}^{2} + 2as }}}</p><p>$

$</p><p></p><p>\mapsto \sf\boxed{\bold{\pink{s = \frac{v {}^{2} - u {}^{2} }{2a} }}}</p><p></p><p>$

$\longmapsto\tt \: \frac{(20) {}^{2} - (10) {}^{2} }{2 \times 15}$

$\longmapsto\tt \frac{400 - 100}{30}$

$\longmapsto\tt{\dfrac{300}{{\cancel{30}}}}$

$</p><p></p><p>\mapsto \sf\boxed{\bold{\red{s = 10m }}}</p><p></p><p>$

$</p><p></p><p>\mapsto \sf\boxed{\bold{\blue{ Displacement\: s = 10m }}}</p><p></p><p>$

Answer 2

$\sf\small{ \underline{\underline\red{ \pmb{Given:-}}}}$

From the given data we have:-

• Initial velocity (u) = 5 m/s
• Final velocity (v) = 10 m/s
• Acceleration (a) = 15 m/s²

$\sf\small{ \underline{\underline\red{ \pmb{To \: find:-}}}}$

• Find the displacement.

$\sf\small{ \underline{\underline\red{ \pmb{ Solution :-}}}}$

Now using second equation of motion :-

$\leadsto \underline{ \boxed{ \purple{ \sf{v}^{2} = {u}^{2} + 2as }}}$

Substituting values

$\sf \longrightarrow \: {(20)}^{2} = {(10)}^{2} + 2 \times 15 \times s$

$\sf \longrightarrow 400 = 100 + 30s$

$\sf \longrightarrow 400 - 100 = 30s$

$\sf \longrightarrow 300 = 30s$

$\sf \longrightarrow s = \cancel \frac{300}{30}$

$\sf \longrightarrow s = 10 \: m$

So, Displacement is 10 m.

$\pink{ - - - - - - - - - - - - - - - - }$

Equations of motion :

$\large\leadsto \boxed{ \pink{ \sf \: v = u + at }}$

$\large\leadsto\boxed{ \pink{ \sf{v}^{2} = {u}^{2} + 2as}}$

$\large\leadsto \boxed{ \pink{ \sf s=ut + ½ at² }}$