Motion with Constant Acceleration

Manual: General · Subject: Newtonian Mechanics

Use kinematic equations to solve straight-line motion when acceleration is constant.

When Acceleration Does Not Change

If acceleration is constant, motion in one dimension can be described with a small set of equations. These are called kinematic equations.

For constant acceleration $a$ , the equations are $v = v_0 + at$ , $x = x_0 + v_0 t + \frac{1}{2}at^2$ , and $v^2 = v_0^2 + 2a(x-x_0)$ .

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What the symbols mean

Here $x_0$ and $v_0$ are the initial position and velocity, and $t$ is elapsed time. These equations work only when acceleration is constant.

Near Earth’s surface, an object in free fall has acceleration approximately equal to $g \approx 9.8\,m/s^2$ downward, ignoring air resistance.

Which equation relates velocity to time for constant acceleration?

v = v0 + at x = x0 + v0 t + 1/2 at^2 F = ma W = mg

If acceleration is constant, what is the shape of the velocity-time graph?

Equation selection guide