Particle Motion and Velocity

Flashcards covering key concepts related to particle motion, including definitions and mathematical expressions for velocity, acceleration, displacement, and critical points.

Particle at rest

When the velocity of the particle is zero: $v(t) = 0$.

Particle moving to the right

When the velocity of the particle is positive: v(t) > 0.

Particle moving to the left

When the velocity of the particle is negative: v(t) < 0.

Change in direction

Occurs when the velocity of the particle changes signs.

Instantaneous velocity

The velocity of the particle at a specific time.

Acceleration of the particle

The rate of change of velocity at a specific time.

Speed of the particle increasing

When velocity and acceleration have the same sign: either v(t) > 0 and a(t) > 0, or v(t) < 0 and a(t) < 0.

Speed of the particle decreasing

When velocity and acceleration have different signs: either v(t) > 0 and $a(t) < 0$, or $v(t) < 0$ and $a(t) > 0$.

Average velocity

The total distance traveled by the particle divided by the time interval.

Displacement

The net distance traveled by the particle over a time interval.

Position of the particle

The location of the particle at a particular time.

Finding extreme positions

Determining the minimum or maximum value of $s(t)$ over an interval.

Critical points

Values of $t$ where the velocity is zero or does not exist.

Total distance traveled

The integral of the absolute value of velocity over the time interval.

Distance calculation formula

$s(b) - s(a) = ext{Total distance traveled}$.