Answer:
v = 2.45 m/s
Explanation:
given,
mass of the dart = 0.5 Kg
spring constant of the dart = k = 300 N/m
compressed distance = 10 cm = 0.1 m
speed acquire by the cart = ?
we know,
using conservation of energy
kinetic energy will be equal to spring energy
[tex]\dfrac{1}{2}mv^2 = \dfrac{1}{2}kx^2[/tex]
[tex]mv^2 = kx^2[/tex]
[tex]v^2 = \dfrac{kx^2}{m}[/tex]
[tex]v = x\sqrt{\dfrac{k}{m}}[/tex]
[tex]v = 0.1\sqrt{\dfrac{300}{0.5}}[/tex]
[tex]v = 0.1\times 24.495[/tex]
v = 2.45 m/s
speed acquire by the dart is equal to v = 2.45 m/s
