Question

1. if ke is kinetic energy and v is velocity, which of these graphs would be a straight line? a. ke versus v b. ke versus v² c. ke² versus v d. ke² versus v²

Explanation:

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy is $KE = \frac{1}{2}mv^2$, where $m$ is mass (assumed constant for a given object).

Step2: Analyze Relationship for Straight Line

A straight - line graph has the form $y = mx + c$ (linear relationship). If we let $y = KE$ and $x = v^2$, then from $KE=\frac{1}{2}mv^2$, we can rewrite it as $KE=\frac{1}{2}m\times v^2$. Here, $\frac{1}{2}m$ is a constant (slope) and when we plot $KE$ versus $v^2$, the equation is linear ($y = kx$ where $k=\frac{1}{2}m$ and $c = 0$).

• For option A: $KE$ vs $v$ is a quadratic relationship ($KE\propto v^2$), so the graph of $KE$ vs $v$ is a parabola, not a straight line.
• For option C: $KE^2$ vs $v$: Since $KE\propto v^2$, $KE^2\propto v^4$, which is a non - linear relationship, so the graph is not a straight line.
• For option D: $KE^2$ vs $v^2$: Since $KE\propto v^2$, $KE^2\propto v^4$, so $KE^2$ vs $v^2$ is a quadratic relationship (not linear), so the graph is not a straight line.

Answer:

B. $KE$ versus $v^2$