Question

a mass of 0.5 kg moving eith a speed of 1.5 km/s on a horizontal smooth surface collides with a nearly weightless​

Answer 1

$\bf \underline{ \underline{Answer}} : - \\ x = 0.15 \: m \\ \\ \underline{\underline{ \bf{Step - by - step \: explanation}}} : -$

According to the question:-

$mass \: of \: body \: (m) = 0.5 \: kg \\ \\ initial \: speed \: ( u )= 1.5 \: \frac{m}{s} \\and ,force (k) = 50 N\\ \\ now \: here \\ \\ spring \: potential \: energy \: equal \: to \: kinetic \: energy \\ \\ \frac{1}{2} m {u}^{2} = \frac{1}{2} k \: {x}^{2} \\ \\ \implies \: {x}^{2} = \frac{m \: {u}^{2} }{k} \\ \\ \implies \: {x}^{2} = \frac{0.5 \times 1.5 \times 1.5}{50} \\ \\ \implies \:x = 0.15 \: m$