Lesson 7 of 10 · 6 min
Constant acceleration in a plane
NCERT §3.8
The drone keeps the same settings: it started with 4.0 m/s along x and gains 3.0 m/s along y every second. Where will it be at t = 2 s, and how fast will it be flying?
The lesson in notes
In short
If a is constant, v = v₀ + a t and r = r₀ + v₀ t + ½ a t², as vectors.
In components: x = x₀ + v₀ₓ t + ½ aₓ t² and y = y₀ + v₀ᵧ t + ½ aᵧ t², with vₓ = v₀ₓ + aₓ t and vᵧ = v₀ᵧ + aᵧ t.
Motion in a plane with constant acceleration is two independent one-dimensional motions, along x and along y, sharing the same clock t.
Example: starting at the origin with v₀ = 4.0 î m/s and a = 3.0 ĵ m/s², after 2 s the object is at 8.0 î + 6.0 ĵ m, 10 m from the start, moving at 4.0 î + 6.0 ĵ m/s (about 7.2 m/s).
The velocity turns steadily towards the direction of a, while the component perpendicular to a never changes.