Question

solve this .......☺️

Answer 1

________HEY FRIEND!!_______
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» YOUR ANSWER IS "10^-4 kgm^-1"

» OPTION "B" IS THE CORRECT ANSWER

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Answer 2

Hey there !

Solution:

So Kinetic Energy of the particle = $\frac{1}{8}m{v_0}^2$

=> $\frac{1}{2}mv^2 = \frac{1}{8}m{v_0}^2$

m gets cancelled on both sides. We get,

$\frac{1}{2}v^2 = \frac{1}{8}{v_0}^2$

Transposing 2 to the other side we get,

=> $v^2 = \frac{2}{8} {v_0}^2$

=> $v^2 = \frac{ {v_0}^2 }{ 4 }$

Taking Square root on both sides we get,

=> $v = \frac{v_0}{2}$

We know that v₀ = 10. So substituting it we get,

=> $v = \frac{10}2} = 5$

Force = -kv²

=> m.a = -kv²

=> m ∫ $\frac{dv}{dt}$ = - kv²

=> ( 10⁻² ) $\frac{dv}{dt}$ = -kv²

After integrating we get,

=> $\frac{1}{5} - \frac{1}{10} = 100 k ( 10 )$

=> 10⁻¹ = 10³ k

=> 10⁻¹ / 10³ = k

=> 10⁻⁻¹⁻³ = k

=> k = 10⁻⁴ Kg/m.

Hope my answer helped !

( For Intergration steps refer attachment as coding was not available )