Work & Kinetic Energy
Push a cart, see work integral. Builds on Newton's Three Laws.
A car going 30 km/h brakes to a stop. Then the same car going 60 km/h (twice as fast) brakes to a stop using the same brakes.
How much farther does the faster car travel before stopping?
Four times as far! Kinetic energy = ½mv². Double the speed means 4× the kinetic energy. Since the brakes apply the same force, they need 4× the distance to do 4× the work (W = Fd). This is the single most important equation for road safety.
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Push the cart and watch kinetic energy accumulate. See how the work integral equals the change in kinetic energy.
W = ΔKE = ½mv²
Work is a 'process' (force × distance). Kinetic energy is a 'state' (½mv²). The theorem connects them: the journey (work) determines the destination (energy).
At 120 km/h you have 4× the kinetic energy of 60 km/h. Crash force depends on energy, not speed. This is why a 20% speed increase causes a 44% increase in fatal crash risk.
A 90 mph fastball has 50% more kinetic energy than a 73 mph changeup (v² scaling). The extra energy is what makes fast pitches harder to catch and hit farther.
Hitting the 'sweet spot' maximizes energy transfer from racket to ball. Off-center hits waste energy in racket vibration — that's work done on the WRONG object.
“Energy is the currency of physics. Work is how you earn or spend it. And the v² in kinetic energy is why speed is both thrilling and dangerous.”
Work & Energy Lab
Apply forces to a cart and watch kinetic energy build. See the work-energy theorem in real time with animated energy bar graphs.
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Push the cart to 2 m/s, note the KE. Now push to 4 m/s — the KE is 4× larger! Then apply a braking force and watch the KE drain away as work is done.
The area under the Force vs. Distance graph equals the work done. This area equals the change in kinetic energy — always, exactly, guaranteed.