Constant-Acceleration Kinematics in a Plane
For constant vector acceleration a, v(t) = v_0 + at and r(t) = r_0 + v_0 t + one-half at squared; eliminating time or applying components gives the required geometry.
Why this shows up in the exam
Vehicle motion with independent horizontal and vertical acceleration · Locating particles under constant force · Reconstructing a trajectory from component equations
Learn the idea
With constant acceleration, each Cartesian component follows the familiar one-dimensional equations independently. A planar path may curve even though the acceleration is constant, because the horizontal and vertical velocity components evolve separately and then recombine.
🧠 Memory hook: Constant acceleration means two independent quadratic component stories.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v_vector = v₀_vector + a_vector t — velocity under constant acceleration
- r_vector = r₀_vector + v₀_vector t + (1/2)a_vector t² — position under constant acceleration
- v² = v₀² + 2 a dot (r-r₀) — scalar relation only when applied consistently along the displacement
How to approach it
- 1Choose axes that simplify acceleration
- 2Write one equation per component
- 3Use the common time to reconnect the components
Common slip-ups that cost marks
- •Applying a scalar equation to vector magnitudes blindly
- •Omitting initial position
- •Mixing components from different times
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A particle has initial speed 2 m/s and constant acceleration 3 m/s^2 for 4 s. What distance does it cover?
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