EQUATION

Position–Time Relation

Gives the displacement of an object under constant acceleration after a time t

§ 01

The equation

EQ.POSITION-TIME-RELATION

d = v_0 t + \tfrac{1}{2}at^2

§ 02

What it solves

Gives the displacement of an object under constant acceleration after a time t. Use it when you need distance traveled and do not know — or want to avoid finding — the final velocity.

§ 03

When to use it

Constant-acceleration rectilinear motion. Applies equally to vertical free-fall (a = g downward) and horizontal braking problems.

§ 04

When NOT to use it

Breaks down when acceleration changes with time. Gives displacement, not total path length, so it can mislead if the object reverses direction.

§ 05

Common mistakes

Using total time T instead of the sub-interval time t. Forgetting the ½ factor, which doubles the answer. Substituting distance for displacement — if the object turns around, the equation still gives the net displacement, not the odometer reading.

§ 06

Topics that use this equation

motion in a straight line