Kinematic equations

Gist: When acceleration is constant, position is a quadratic in time — and the three coefficients turn out to be the initial position, the initial velocity, and half the acceleration.

$x=c_1+c_{2}t+c_3{t}^{2}v=c_2+2c_{3}ta=2c_3$

$c_1=x_0{c}_2=v_0{c}_3=\frac{1}{2}a$

Why it matters: Differentiate twice and the constants fall out with physical meaning attached. Worked in the lecture as $x=8-6t+t^2$, giving $v=-6+2t$ and $a=2$ — noted there as the shape of a single segment in motion planning.

Detail: Lecture 2, p.5

Related: Instantaneous acceleration, Free fall, Physics