Question

What is the core concept in constant acceleration

Answer 1

The core concept in constant acceleration is that the acceleration a is the same at every instant (constant in magnitude and direction). That makes velocity change at a steady (linear) rate and position change quadratically in time. From that you get three standard kinematic relations (for one-dimensional motion):

- v = v0 + a t (velocity changes linearly with time)
- x = x0 + v0 t + 1/2 a t^2 (position is a quadratic function of time)
- v^2 = v0^2 + 2 a (x − x0) (relates speed to displacement without time)

Also, when a is constant the average velocity over an interval is (v0 + v)/2, because the velocity-time graph is a straight line.

Key points:
- Acceleration = dv/dt; constant a ⇒ v(t) is linear in t.
- Displacement is the area under the velocity–time graph.
- These formulas assume a is constant in magnitude and direction (vectors matter).
- Example: from rest (v0 = 0) with a = 2 m/s^2 for t = 5 s: v = 10 m/s and x − x0 = 0.5·2·25 = 25 m.

Common real-world example: near Earth's surface, free-fall acceleration ≈ 9.8 m/s^2 downward (approximately constant).