Translatory Motion and Kinematic Equations

A set of vocabulary flashcards covering the three equations of motion, velocity-time graph analysis, free-fall motion, and projectile motion based on Unit 3 Translatory Motion.

First Equation of Motion

The equation $v_f = v_i + at$, representing the relation between initial velocity ($v_i$), final velocity ($v_f$), acceleration ($a$), and time ($t$).

Second Equation of Motion

The equation $S = v_i t + \frac{1}{2} a t^2$, representing the relation between initial velocity ($v_i$), acceleration ($a$), distance ($S$), and time ($t$).

Third Equation of Motion

The equation $2aS = v_f^2 - v_i^2$, representing the relation between initial velocity ($v_i$), final velocity ($v_f$), acceleration ($a$), and distance ($S$).

Velocity-Time Graph for Constant Acceleration

A graphical representation of motion where line segment $AB$ represents uniform acceleration $a$, line segment $OA$ represents initial velocity $v_i$, line segment $BD$ represents final velocity $v_f$, and line segment $OD$ represents time $t$.

Slope of Velocity-Time Graph

The slope represented by $a = \frac{BC}{AC} = \frac{BD - CD}{OD}$, which gives the acceleration of a moving body.

Total Distance Travelled (Velocity-Time Graph)

The total area under the velocity-time graph equal to the area of trapezium $OABD$, calculated as $S = \frac{1}{2}(\text{sum of parallel sides}) \times (\text{distance between the parallel sides}) = \frac{1}{2}(OA + BD) \times OD$.

Free-Fall Motion

An example of uniformly accelerated motion where all objects (lighter or heavier) fall freely near the surface of the Earth with the same acceleration, independent of their masses, in the absence of air resistance.

Acceleration Due to Gravity

The uniform acceleration experienced by a free-falling body, denoted by $g$, directed towards the centre of the Earth, with a value of $9.81\,m\,s^{-2}$.

First Equation of Motion for Free-Fall

The kinematic equation $v_f = v_i + gt$, obtained by replacing acceleration $a$ with acceleration due to gravity $g$.

Second Equation of Motion for Free-Fall

The kinematic equation $h = v_i t + \frac{1}{2} g t^2$, obtained by replacing distance $S$ with height $h$ and acceleration $a$ with $g$.

Third Equation of Motion for Free-Fall

The kinematic equation $2gh = v_f^2 - v_i^2$, obtained by replacing distance $S$ with height $h$ and acceleration $a$ with $g$.

Projectile Motion

The motion of a body along a curved path in a plane having both vertical and horizontal components under the influence of gravitational force.

Trajectory

The curved path followed by a body undergoing projectile motion in a plane.