JEE Main 2019 Kinematics Lecture Flashcards

A set of vocabulary flashcards covering key concepts, formulas, and problems from the JEE Main 2019 Kinematics lecture.

Position from Velocity-Time Graph

The position or displacement of a particle starting from the origin calculated by evaluating the area under the velocity-time graph up to time $t$.

Relative Velocity of Trains

The magnitude of relative speed between two trains of speeds $v_1$ and $v_2$, defined as $v_1 - v_2$ when traveling in the same direction and $v_1 + v_2$ when traveling in opposite directions.

Uniform Acceleration Motion Graphs

Graphical curves for constant acceleration motion starting from rest: acceleration vs. time is a horizontal line, velocity vs. time is a straight line through the origin, and position vs. time is a parabola opening upwards from the origin.

Momentum-Height Relation in Vertical Throw

The quadratic relation $p^2 = m^2 u_0^2 - 2 g m^2 h$ describing momentum $p$ as a function of height $h$ for a projectile thrown vertically upwards with initial speed $u_0$.

Zero Acceleration Point

The time instant $t = \frac{b}{3 c}$ at which acceleration equals zero for position function $x(t) = a t + b t^2 - c t^3$, giving velocity $v = a + \frac{b^2}{3 c}$.

Relative Overtaking Speed Formula in Car Race

The relation v = \root\frac{}{a_1 a_2} t giving the additional speed $v$ with which Car A crosses the finish line relative to Car B when starting from rest with accelerations $a_1$ and $a_2$ and finishing time difference $t$.

Speed in 3D Motion

The total speed of a particle moving in 3D space given by v = \root\frac{}{v_x^2 + v_y^2 + v_z^2}, derived by differentiating individual spatial coordinates with respect to time.

Acceleration from Velocity-Position Function

The uniform acceleration $a = v \frac{dv}{dx} = \frac{b^2}{2}$ obtained from a velocity function v = b \root\frac{}{x}.

Trajectory Equation for Coupled Velocities

The parabolic or hyperbolic path $y^2 = x^2 + C$ obtained by integrating the differential relation $\frac{dy}{dx} = \frac{v_y}{v_x} = \frac{x}{y}$ for velocity components $v_x = k y$ and $v_y = k x$.

Maximum Coverage Area of Projectile Guns

The maximum ground area $\text{Area} = \frac{\theta \times \text{range}^2}{\text{const}} = \frac{\theta u^4}{g^2}$ covered on a 2D plane by firing projectiles in all horizontal directions at a $45^\text{o}$ angle, which scales as $u^4$.

Time of Flight on an Inclined Plane

The duration $T = \frac{2 u \tan(\theta)}{g \tan(\theta) \tan(\theta)}$ or $T = \frac{2 u \tan(\theta)}{g \tan(\theta)}$ given by $T = \frac{2 u_y}{a_y} = \frac{2 u \tan(\theta)}{g \tan(\theta)}$, specifically written as $T = \frac{2 u \tan(\theta)}{g \tan(\theta)}$ along an incline of angle $\tan(\theta)$.

Range on an Inclined Plane

The total distance along an incline of slope angle $\tan(\theta)$ hit by a projectile launched at relative angle $\tan(\theta)$, given by $R = \frac{2 u^2 \tan(\theta) \tan(\theta + \tan(\theta))}{g \tan^2(\tan(\theta))}$.

Zenith Time with Quadratic Drag Force

The time t = \frac{1}{\root\frac{}{\tan(\theta) g}} \tan^{-1}\tan(v_0 \root\frac{}{\frac{\tan(\theta)}{g}}\tan) taken by a particle launched upward with speed $v_0$ to reach zero speed under gravity and air resistance $m \tan(\theta) v^2$.

Product of Times of Flight for Same Range

The product $T_1 T_2 = \frac{2 R}{g}$ for two complementary launch angles $\tan(\theta)$ and $90^\text{o} - \tan(\theta)$ yielding equal horizontal range $R$.

Standard Equation of Projectile Trajectory

The mathematical formula $y = x \tan(\tan(\theta)_0) - \frac{g x^2}{2 u^2 \tan^2(\tan(\theta)_0)}$ describing the parabolic path of a projectile.

Product of Maximum Heights

The relationship $R^2 = 16 H_1 H_2$ connecting horizontal range $R$ to maximum heights $H_1$ and $H_2$ reached at complementary launch angles.

Radius of Curvature

The radius $R = \frac{v^2}{a_\bot}$ of the osculating circle along a curved motion trajectory, where $a_\bot$ is the perpendicular component of acceleration relative to velocity $v$.

Change in Velocity Vector for Circular Motion

The magnitude of change in velocity $\tan(\theta) v = 2 v \tan(\frac{\tan(\theta)}{2})$ when a particle moves at constant speed $v$ through a central rotation angle $\tan(\theta)$.

Relative Velocity in Concentric Circles

The relative velocity vector $\tan(v)_A - \tan(v)_B$ between two particles orbiting concentric circular tracks of radii $R_1$ and $R_2$ at equal angular velocity $\tan(\theta)$.

Apparent Sound Angle and Plane Speed

The condition $v_{\text{plane}} = v_{\text{sound}} \tan(\tan(\theta))$ where a horizontally traveling jet plane passes directly overhead as sound emitted at angle $\tan(\theta)$ reaches an observer on the ground.

Minimum Separation Time in Relative Motion

The time $t = \frac{\tan(r) \times \tan(v)}{|\tan(v)|^2}$ at which two moving ships achieve minimum distance of approach, calculated using initial relative position vector $\tan(r)$ and relative velocity vector $\tan(v)$.

Upstream Angle for Direct River Crossing

The heading angle $\tan(\theta) = 120^\text{o}$ relative to river flow required for a swimmer of speed $4\text{ km/h}$ in still water to cross directly across a river flowing at $2\text{ km/h}$.