Physics Class 11: Motion in a Plane Formulas

Study Notes

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

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}).

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}).

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)).

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)

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

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).