## You are here

Now I'll get to your comment. You mentioned the work-energy theorem, so let's clarify that it's $W_{ext} = \Delta KE$, not the expression written in your comment. [edit: earlier comments about the Earth don't apply. I hadn't actually looked up the problem.] You could consider the car-spring as a single system, which is all well and good, but this isn't strategic for problem solving since your only conclusion would be that $W_{ext} = 0$. This problem is asking for the spring constant, and conservation of energy is the ticket to solving for it. Maybe you would prefer the following expression, rather than the one I wrote in the video:
$KE_1 + PE_1 + W_{NC} = KE_2 + PE_2$. $W_{NC}$ typically represents friction, which is zero in this case, so we plug different types of energy into this expression and get $\dfrac{1}{2}mv_i^2 + 0 + 0 = 0 + \dfrac{1}{2}kx^2$ where I've substituted specific expressions in the same order as the equation before that has more generic expressions. This will arrive at $\dfrac{1}{2}mv_i^2 = \dfrac{1}{2}kx^2$, which is the same as in the video.