which graph best represents the relationship between ke and speed? ke speed ke speed ke speed ke speed

Explanation:

Step1: Recall kinetic - energy formula

The kinetic - energy formula is $KE=\frac{1}{2}mv^{2}$, where $m$ is the mass of the object and $v$ is the speed. Since mass $m$ is a non - zero constant for a given object, $KE$ is a quadratic function of $v$.

Step2: Analyze the form of the quadratic function

The general form of a quadratic function $y = ax^{2}+bx + c$ (in our case, $y = KE$, $x = v$, $a=\frac{1}{2}m$, $b = 0$, $c = 0$). A quadratic function $y=ax^{2}$ with $a>0$ has a parabolic shape opening upwards. When $v = 0$, $KE=0$, and as $v$ increases (either in the positive or negative direction), $KE$ increases.

Answer:

The graph that is a parabolic curve opening upwards (the second graph from the left) best represents the relationship between $KE$ and speed.