Equations of Motion

For uniformly accelerated motion in a straight line: v = u + at, s = ut + ½at², v² = u² + 2as. Here u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time.

First equation: v = u + at

For motion with constant acceleration a, the final velocity v after time t is v = u + at, where u is the initial velocity. This comes from the definition of acceleration: a = (v − u) / t. It relates velocity and time.

Second equation: s = ut + ½at²

The displacement s in time t for an object starting with velocity u and having constant acceleration a is s = ut + ½at². When a = 0, this gives s = ut (uniform motion). The term ½at² is the extra displacement due to acceleration.

Third equation: v² = u² + 2as

This equation relates v, u, a, and s without involving time: v² = u² + 2as. It is useful when time is unknown. For free fall from rest, u = 0 and a = g, so v² = 2gs. These three equations are sufficient to solve problems in one-dimensional uniformly accelerated motion.

Link to simulator: The motion in the simulator can be described by these equations when acceleration is constant.

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