Translational Kinetic Energy
An object in motion carries energy, and the formula is brutally simple: $K = \dfrac{1}{2}mv^2$. Brutally simple, and brutally easy to misread. The $v$ is squared, so doubling the speed quadruples $K$. The output is a scalar, with no direction, even when the velocity is a vector. And $v$ depends on the observer, so $K$ does too: a passenger sitting still on a moving train has $K = 0$ in the train's frame and $K > 0$ in the ground frame. Both observers are right.
Three pitfalls. Students assume linear scaling and double $K$ when speed doubles, missing the quadratic. They write $K$ with a direction ("16 J to the right"), forgetting the formula squares a magnitude and leaves no room for an arrow. And they treat $K$ as a property the object carries, the same value for every observer, when in fact $K$ is frame-dependent: same ball, same mass, different speed, different $K$. The lesson walks all three.
The work
3 ways in · any order
Lesson
Translational Kinetic Energy
›
Read the lesson. The formula and one worked example, then two surprises (quadratic scaling in $v$, frame-dependence of $K$) and three pitfalls, followed by a ten-scenario applet that drills the linear-scaling trap, the scalar-not-vector category error, and the frame-dependence of $K$.
Diagnostic
10-item topic check
›
Ten multiple-choice items on the $v^2$ scaling traps, the scalar-not-vector category error, and the frame-dependence of $K$. Each distractor maps to a specific misconception so the targeted-practice round can drill exactly what you missed.
Targeted Practice
Drill a single misconception
›
Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.