Answer:
The initial velocity of the cart was 0.91m/s.
Explanation:
When the car comes to a stop it has delivered all of its kinetic energy to the spring; therefore,
[tex]\dfrac{1}{2}kx^2 = \dfrac{1}{2} mv^2[/tex]
solving for [tex]v[/tex] we get:
[tex]v = x\sqrt{\dfrac{k}{m} },\\[/tex]
we put in [tex]k = 4.21*10^{5}N/m[/tex], [tex]m = 5.18*10^{4}kg[/tex], and [tex]x = 0.32m[/tex] to get:
[tex]v = (0.32m)\sqrt{\dfrac{4.21*10^5}{5.18*10^4} },\\[/tex]
[tex]\boxed{v = 0.91m/s.}[/tex]
