Position, Velocity, and Acceleration along the x-axis

Vocabulary flashcards covering key definitions, formulas, and conditions for position, velocity, and acceleration for motion along the x-axis.

Initially

$$t = 0$$

At rest

$$v(t) = 0$$

At the origin

$$x(t) = 0$$

Particle changes directions

Occurs when velocity changes signs.

Velocity is positive

Particle is moving right (or up)

Velocity is negative

Particle is moving left (or down)

Average velocity (Given $v(t)$)

$\frac{1}{b - a} \int_a^b v(t)\,dt$ (the average value of the velocity function)

Average rate of change of velocity

$$\frac{v(t_2) - v(t_1)}{t_2 - t_1}$$

Average Acceleration (Given $a(t)$)

$\frac{1}{b - a} \int_a^b a(t)\,dt$ (the average value of the acceleration function)

Average rate of change of acceleration

$$\frac{a(t_2) - a(t_1)}{t_2 - t_1}$$

Instantaneous velocity

Velocity at an exact moment

Positive acceleration

Velocity is increasing

Negative acceleration

Velocity is decreasing

Speed increasing (Speeding up)

Velocity and acceleration have the same sign: $v(t) > 0$ and $a(t) > 0$; or $v(t) < 0$ and $a(t) < 0$

New position

$$s(a) + \int_a^b v(t)\,dt$$