Distance in uniformly variable motion

In uniformly variable motion the velocity changes evenly, so the average velocity equals the half-sum of the initial and final velocities: υ_avg = (υ₀ + υ)/2. Hence s = (υ₀ + υ)t/2. Substituting υ = υ₀ + at gives s = υ₀t + at²/2. Starting from rest (υ₀ = 0) it becomes s = at²/2: the distance is directly proportional to the square of time, so doubling the time makes the distance 4 times larger. The distance–time graph is then a parabola (a curve that gets steeper and steeper upward). The distance can also be found from the velocity graph: the area of the figure under the graph is numerically equal to the distance covered.