Physics Class 11: Motion in a Plane Formulas

Study Notes

Displacement Vector

Displacement vector is defined as the difference between two position vectors: (\vec{r} = \vec{r}_2 - \vec{r}_1).

Velocity

Average velocity formula calculates the change in displacement over the change in time: (\vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t}).
Instantaneous velocity is the derivative of the displacement with respect to time: (\vec{v} = \frac{d\vec{r}}{dt}).

Acceleration

Average acceleration is found by dividing the change in velocity by the change in time: (\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}).
Instantaneous acceleration is obtained by differentiating velocity with respect to time: (\vec{a} = \frac{d\vec{v}}{dt}).

Equations of Motion (Constant Acceleration)

The position-time relationship is expressed as: (\vec{r} = \vec{r}_0 + \vec{v}_0 t + \frac{1}{2} \vec{a} t^2).
The velocity-time relationship is defined as: (\vec{v} = \vec{v}_0 + \vec{a} t).
The velocity-displacement relationship can be written as: (\vec{v}^2 = \vec{v}_0^2 + 2 \vec{a} \cdot (\vec{r} - \vec{r}_0)).

Projectile Motion

The horizontal range of a projectile is determined by the formula: (R = \frac{v_0^2 \sin(2\theta)}{g}).
Maximum height can be determined using: (H = \frac{v_0^2 \sin^2(\theta)}{2g}).
Time of flight for a projectile in motion is calculated by: (T = \frac{2 v_0 \sin(\theta)}{g}).
The position of a projectile at time (t) can be described with:
- Horizontal position: (x = v_0 \cos(\theta) t)
- Vertical position: (y = v_0 \sin(\theta) t - \frac{1}{2} g t^2)

Relative Velocity

The relative velocity of one object (A) with respect to another object (B) is given by: (\vec{v}_{A/B} = \vec{v}_A - \vec{v}_B).

Centripetal Acceleration (Circular Motion)

Centripetal acceleration relates the tangential velocity to the radius of the circular path: (a_c = \frac{v^2}{r}).

Uniform Circular Motion

Angular displacement over time is defined by: (\theta = \omega t).
Angular velocity is calculated as: (\omega = \frac{d\theta}{dt}).
Angular acceleration is the rate of change of angular velocity: (\alpha = \frac{d\omega}{dt}).
Tangential velocity in circular motion relates to angular velocity and radius by: (v = \omega r).
Tangential acceleration is determined by: (a_t = \alpha r).

Description

Test your understanding of the crucial formulas related to motion in a plane for Class 11 Physics. This quiz covers key concepts such as displacement, velocity, and acceleration, along with their mathematical representations. Use this resource to reinforce your knowledge and preparation for exams.