Motion in a plane – position, velocity and acceleration vectors on a curved path
PhysicsKinematicsAges 15–16
Loading…
Sign in to play
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Kinematics
An object moves along a curved path that you reshape by dragging points. Position vectors at two instants give the displacement Δr, and shrinking Δt turns the average velocity Δr/Δt into the instantaneous velocity, tangent to the path. The Acceleration screen splits a into its tangential component a_t = dv/dt and normal component a_n = v²/R, with the circle of curvature, and the Graphs screen plots x(t), y(t), vx(t) and vy(t).
Lesson: Motion in two dimensions: position, velocity and acceleration vectors; tangential and normal acceleration
What it shows
Position is a vector r drawn from a fixed origin. Between two instants the displacement is Δr = r₂ − r₁, and the average velocity Δr/Δt points along the chord. As Δt shrinks, the chord turns into the tangent, so the instantaneous velocity v = dr/dt is always tangent to the path. Acceleration has two parts: a tangential component a_t = dv/dt that changes the speed, and a normal component a_n = v²/R, towards the centre of curvature, that changes the direction. In the model the object moves with a constant a_t along a smooth spline or a circle.
How to use
On Displacement and velocity, set Time t, then lower the Time interval Δt from 1 s towards 0.01 s, pressing Record each time, and watch Δr/Δt line up with v. On Acceleration, change the Tangential acceleration a_t and drag the blue points to bend the Path, then compare a_t with a_n. On Graphs, press Run and relate the slope of x(t) to vx.
Parameters you can change
- Screen Displacement and velocity, Acceleration, Graphs
- Path S-bend, Hairpin, Circle
- Radius of the circle 1–2.8 m
- Initial speed 0.2–5 m/s
- Tangential acceleration -1–1 m/s²
- Time t 0–200 s
- Time interval Δt 0.01–2 s
- Dots every 0.5 s
- Circle of curvature
Questions to explore
- Why does the average velocity Δr/Δt turn towards the tangent as Δt gets smaller?
- When an object follows a curve at constant speed, why is its acceleration not zero, and which way does it point?
- At the same speed, where on a path is the normal acceleration largest, and why?
