1D Kinematics
Drag a car, see x(t), v(t), a(t) graphs.
A car travels at 60 km/h for the first half of the trip's DISTANCE, then at 30 km/h for the second half of the DISTANCE.
What is the car's average speed for the entire trip?
If each half is distance d: time₁ = d/60, time₂ = d/30. Total time = d/60 + d/30 = d/20. Average speed = 2d / (d/20) = 40 km/h. The car spends TWICE as long going slow!
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Set the initial velocity and acceleration (or pick a preset) and watch the position, velocity, and acceleration graphs update in real time.
x = x₀ + v₀t + ½at²
This one equation describes everything from a dropped ball to a launching rocket — as long as acceleration is constant.
Police radar measures instantaneous velocity, not average speed. You can average 60 mph while hitting 90 at one point.
Usain Bolt's average speed was 37.6 km/h but his peak was 44.7 km/h. The acceleration phase at the start drags the average down.
At 60 mph, doubling your speed requires FOUR times the stopping distance (because d ∝ v²). That's why speeding is so dangerous.
“Position, velocity, acceleration — they're not three separate things. They're the same story told at three levels: where you are, how fast you're moving, and how that's changing.”
Motion Designer
Create any motion profile by adjusting acceleration over time. Watch the car follow your instructions.
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Create a trip where the car accelerates, cruises, then brakes. Compare the graphs.
The area under the v(t) curve equals the displacement. The area under the a(t) curve equals the velocity change.