Question

which graph best represents the relationship between ke and speed?

Explanation:

Step1: Recall KE formula

Kinetic Energy (KE) formula: $KE = \frac{1}{2}mv^2$ (where $m$ is mass, $v$ is speed).

Step2: Analyze relationship

KE is proportional to $v^2$ (quadratic relationship). A quadratic function $y = ax^2$ (here $y=KE$, $x=speed$) has a parabolic (curved, increasing with increasing slope) graph.

• First graph: Linear (straight line) – incorrect (KE ∝ $v^2$, not linear).
• Second graph: Curved, increasing with steeper slope (matches $v^2$ growth) – correct.
• Third graph: Linear decreasing – incorrect.
• Fourth graph: Parabola opening down – incorrect (KE increases with speed, no maximum in positive speed range).

Answer:

The second graph (the one with the upward - curving line, increasing KE as speed increases with a steeper slope as speed rises)