Question

interpreting graphs for ke and mass
which graph best represents the relationship between ke and mass?
four graphs (with ke on y - axis, mass on x - axis) and selection circles below the graphs are shown, with the first graph having a linear upward - sloping line with data points, the second a curved upward - sloping line, the third a linear downward - sloping line, and the fourth a peak - shaped line

Explanation:

Step1: Recall KE formula

The formula for kinetic energy (KE) is $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity. If velocity is constant, KE is directly proportional to mass ($KE \propto m$ when $v$ is constant), so the graph of KE vs. mass should be a straight line with a positive slope (linear relationship).

Step2: Analyze each graph

• First graph: Straight line with positive slope (linear, increasing), matches $KE \propto m$ (if $v$ constant).
• Second graph: Curved (non - linear), doesn't match direct proportionality.
• Third graph: Straight line with negative slope (decreasing), contradicts $KE \propto m$.
• Fourth graph: Parabolic (peaks then drops), contradicts the relationship.

Answer:

The first graph (the one with the straight line increasing as mass increases)