physics-class-11-unit-03-chapter-02-introduction-to-kinematics-basic-mathematical-concepts-l-2-3-tujt-dhbaka

### <Success style="font-size:25px"> Introduction To Kinematics Basic Mathematical Concepts L-2 </Success>
### <primary style="font-size:24px"> Coordinate System </primary>
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- Cartesian axes (x, y)

- We take two mutually perpendicular directions.

- x and y are at an angle of 90 degrees to each other.

- The intersection of these is called the origin represented by O.

- Any point P, which is at a location on the cartesian plane, is described by the coordinates of x and y.

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<footer style = "font-size: 18px">Introduction to Kinematics Basic mathematical Concepts $\rightarrow$ Some Basic Mathematical Concepts $\rightarrow$ <span style = "color:blue"> Coordinate System </span> $\rightarrow$ Position Vector $\rightarrow$ Vector </footer>

### <Success style="font-size:25px"> Introduction To Kinematics Basic Mathematical Concepts L-2 </Success>
### <primary style="font-size:24px"> Position Vector </primary>
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- Position $P$ of a point is given by coordinates$(x, y)$

- $\overrightarrow{O P}$ from origin to length from origin to position of P.

- $\overrightarrow{O P} \rightarrow$ Position vector 
 
- Lenght $OP \rightarrow$ Magnitude.

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<img src='https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/17c8ece1-1131-4b2b-e5e4-58abf49dd600/public'/>

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<footer style = "font-size: 18px">Some Basic Mathematical Concepts $\rightarrow$ Coordinate System $\rightarrow$ <span style = "color:blue"> Position Vector </span> $\rightarrow$ Vector $\rightarrow$ Differential Calculus </footer>

### <Success style="font-size:25px"> Introduction To Kinematics Basic Mathematical Concepts L-2 </Success>
### <primary style="font-size:24px"> Differential Calculus </primary>
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- <span style="color:green">Concept of a derivative</span>

- $y=f(x)$, $y$ is a function of $x$.

- For different values of x, we have different values of y.

- $ P(x, y) $, $Q(x+\Delta x, y+\Delta y)$

- Straight line joining $P Q$

- $\tan \theta=\frac{\Delta y}{\Delta x}$.

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<footer style = "font-size: 18px">Position Vector $\rightarrow$ Vector $\rightarrow$ <span style = "color:blue"> Differential Calculus </span> $\rightarrow$ Slope of a Curve $\rightarrow$ Derivative </footer>

### <Success style="font-size:25px"> Introduction To Kinematics Basic Mathematical Concepts L-2 </Success>
### <primary style="font-size:24px"> Velocity And Acceleration </primary>
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- Path At time t

- $\overrightarrow{O P}=\vec{r}(t)$

- $t+\Delta t$

- Particle at P'

- $\overrightarrow{O P^{\prime}}=\overrightarrow{r^{\prime}}(t+\Delta t)$

- At time $t$, point $P$.

- $\overrightarrow{PP'} \rightarrow$ Displacement vector.

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<img src='https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/08a4d449-928f-4802-d473-f60bbd628300/public'/>

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<footer style = "font-size: 18px">Reference Frame $\rightarrow$ Reference Frame $\rightarrow$ <span style = "color:blue"> Velocity And Acceleration </span> $\rightarrow$ Velocity And Acceleration $\rightarrow$ Motion in a Straight Line </footer>

### <Success style="font-size:25px"> Introduction To Kinematics Basic Mathematical Concepts L-2 </Success>
### <primary style="font-size:24px"> Velocity And Acceleration </primary>
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- $\operatorname{lim}_{\Delta t \rightarrow 0} \frac{\vec{r}(t+\Delta t)-\vec{r}(t)}{\Delta t}$ 
- $=\vec{v}(t) $

- $ \vec{V}_p(\text { at time t})$ = Derivative of position vector

- Acceleration of point $P$ :
- $\overrightarrow{a_p}= \operatorname{lim}_{\Delta t \rightarrow 0} \frac{{\overrightarrow{V_p}(t+\Delta t)-\overrightarrow{V_p}(t)}}{\Delta t}$.

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<footer style = "font-size: 18px">Reference Frame $\rightarrow$ Velocity And Acceleration $\rightarrow$ <span style = "color:blue"> Velocity And Acceleration </span> $\rightarrow$ Motion in a Straight Line $\rightarrow$ Motion in a Straight Line </footer>

### <Success style="font-size:25px"> Introduction To Kinematics Basic Mathematical Concepts L-2 </Success>
### <primary style="font-size:24px"> Displacement </primary>
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- Displacement can be positive and negative.

- Positive $\rightarrow$ if particle moves along ${x}$-axis.

- Negative if paricle move against x axis.

- Moving along $-x$ axis.

- Displacement is a vector quantity.

- In one dimensional motion, direction of displacement is given by the sign,  is positive then it is along + x axis and if it is negative then it is along - x axis.

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<footer style = "font-size: 18px">Problem $\rightarrow$ Analysis $\rightarrow$ <span style = "color:blue"> Displacement </span> $\rightarrow$ Thank You $\rightarrow$  </footer>