physics-class-11-unit-03-chapter-01-frame-of-reference-motion-in-a-straight-line-uniform-lecture-1-3-zjhtgc8aqtk

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Graphical description of displacement v/s time </primary>
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- Straight line equal distance in equal interval of time.

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<footer style = "font-size: 18px"> $\rightarrow$ Frame of Reference, Motion in a Straight Line, Uniform Motion $\rightarrow$ <span style = "color:blue"> Graphical description of displacement v/s time </span> $\rightarrow$ Uniform Motion $\rightarrow$ Uniform Motion </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Motion </primary>
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- **Motion could be more complex**

- Car which starts from rest, starts to move, then it moves ot uniform motion,

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<footer style = "font-size: 18px">Frame of Reference, Motion in a Straight Line, Uniform Motion $\rightarrow$ Graphical description of displacement v/s time $\rightarrow$ <span style = "color:blue"> Uniform Motion </span> $\rightarrow$ Uniform Motion $\rightarrow$ Average velocity </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Motion </primary>
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- How fast is position changing with time?

- speed, include directional aspect $\rightarrow$ velocity

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<footer style = "font-size: 18px">Graphical description of displacement v/s time $\rightarrow$ Uniform Motion $\rightarrow$ <span style = "color:blue"> Uniform Motion </span> $\rightarrow$ Average velocity $\rightarrow$ Unit of Average velocity </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Average velocity </primary>
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- $\text { Average velocity }=\frac{\text { change in displacement }}{\text { change in time }}$

- If the displacement over time interval

- $ \Delta t=\Delta x $

- $ \text { Then average velocity }$

- $\quad$$\quad$$=\frac{\Delta x}{\Delta t} $

- $\quad$$ \bar{V}=\frac{x_2-x_1}{t_2-t_1}$.

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<footer style = "font-size: 18px">Uniform Motion $\rightarrow$ Uniform Motion $\rightarrow$ <span style = "color:blue"> Average velocity </span> $\rightarrow$ Unit of Average velocity $\rightarrow$ Average velocity </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Average velocity </primary>
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- Average velocity $\rightarrow$  vector quantity motion along a straight line $\rightarrow$  direction is given by sign of displacement.

- $ \bar{v}=\frac{x_2-x_1}{t_2-t_1} $

- $ \Delta t=t_2-t_1 $

- $ P Q \rightarrow \text { Straight line } $

- $ \text { Slope of line } $

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<footer style = "font-size: 18px">Average velocity $\rightarrow$ Unit of Average velocity $\rightarrow$ <span style = "color:blue"> Average velocity </span> $\rightarrow$ Slope of Line $\rightarrow$ Instantaneous Velocity and Speed </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Instantaneous Velocity and Speed </primary>
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- $\frac{\Delta x}{\Delta t} \rightarrow$ approach tangent to the $x-t$ curve at $t_1$

- $\text { If } \Delta t \rightarrow 0 .$

- tangent/slope of $x-t$ curve at $t=t$, gives velocity or instantaneous velocity at $t=t_1$

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<footer style = "font-size: 18px">Slope of Line $\rightarrow$ Instantaneous Velocity and Speed $\rightarrow$ <span style = "color:blue"> Instantaneous Velocity and Speed </span> $\rightarrow$ Uniform Motion $\rightarrow$ Instantaneous Velocity and Speed </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Motion </primary>
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- **Motion could be more complex**

- Car which starts from rest, starts to move, then it moves at uniform motion,
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<footer style = "font-size: 18px">Instantaneous Velocity and Speed $\rightarrow$ Instantaneous Velocity and Speed $\rightarrow$ <span style = "color:blue"> Uniform Motion </span> $\rightarrow$ Instantaneous Velocity and Speed $\rightarrow$ Uniform Motion </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Motion </primary>
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- **Motion could be more complex**

- Car which starts from rest, starts to move, then it moves at uniform motion,

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<footer style = "font-size: 18px">Uniform Motion $\rightarrow$ Instantaneous Velocity and Speed $\rightarrow$ <span style = "color:blue"> Uniform Motion </span> $\rightarrow$ Negative Accelerant $\rightarrow$ Displacement </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Negative Accelerant </primary>
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- Curve Upwards

- $\leftarrow$ negative accelerant

- straight line x - t

- ${\Rightarrow} a=0$

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<footer style = "font-size: 18px">Instantaneous Velocity and Speed $\rightarrow$ Uniform Motion $\rightarrow$ <span style = "color:blue"> Negative Accelerant </span> $\rightarrow$ Displacement $\rightarrow$ Displacement </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Displacement </primary>
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- $ x \rightarrow t$

- $ \frac{d x}{d t}=v $

- $ x-t$  curve slope = v

- $ \int{ d x}=\int v d t  $

- $x_2-x_1$

- Area under $v-t$ curve: displacement.

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<footer style = "font-size: 18px">Negative Accelerant $\rightarrow$ Displacement $\rightarrow$ <span style = "color:blue"> Displacement </span> $\rightarrow$ Change of Velocity $\rightarrow$ Chain Rule </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Chain Rule </primary>
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- If acceleration known as a funchon of $x$.

- $\frac{d v}{d t}=a$

- Chain Rule of Differentiation

- $\frac{d v}{d t} =\frac{d v}{d x} \cdot \frac{d x}{d t}= \frac{v d v}{d x} $

- $ =\frac{1}{2} \frac{d}{d x}\left(v^2\right)$.

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<footer style = "font-size: 18px">Displacement $\rightarrow$ Change of Velocity $\rightarrow$ <span style = "color:blue"> Chain Rule </span> $\rightarrow$ Chain Rule $\rightarrow$ Uniform Acceleration </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Chain Rule </primary>
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- $\frac{1}{2} \frac{d}{d x}\left(v^2\right) =a $

- $ \int \frac{1}{2} d\left(v^2\right)  =\int a d x$

- $ \left.\frac{1}{2} v^2\right|_1 ^2  =\int a d x $

- $ =\frac{1}{2}\left(v_2^2-v_1^2\right)$

- $ =\int a d x$.

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<footer style = "font-size: 18px">Change of Velocity $\rightarrow$ Chain Rule $\rightarrow$ <span style = "color:blue"> Chain Rule </span> $\rightarrow$ Uniform Acceleration $\rightarrow$ Uniform Acceleration </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Acceleration </primary>
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- $a=\frac{v-v_0}{t} $

- $ v=v_0+a t $

- Area of triangle = $\frac{1}{2}(v-v_0) t $

- displacement

- Area under $ {v-t}$ curve

- Area $=v_0 t+\frac{1}{2}\left(v- v_0\right) t $

- displacement = $v_0 t+\frac{1}{2} a t^2$

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<footer style = "font-size: 18px">Chain Rule $\rightarrow$ Uniform Acceleration $\rightarrow$ <span style = "color:blue"> Uniform Acceleration </span> $\rightarrow$ Uniform Acceleration $\rightarrow$ Uniform Acceleration </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Acceleration </primary>
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- $a=\frac{v-v_0}{t} $

- $ v=v_0+a t $

- $\frac{1}{2}(v-v_0) t $

- displacement

- Area under $ {v-t}$ curve.

- Area $=v_0 t+\frac{1}{2}\left(v- v_0\right) t $.

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<footer style = "font-size: 18px">Uniform Acceleration $\rightarrow$ Uniform Acceleration $\rightarrow$ <span style = "color:blue"> Uniform Acceleration </span> $\rightarrow$ Uniform Acceleration $\rightarrow$ Uniform Acceleration </footer>

### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Acceleration </primary>
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- $ x  =v_0 t+\frac{1}{2} a t^2 $

- $ x  =\left(\frac{v+v_0}{2}\right) t$

- $ x  =\frac{\left(v+v_0\right)}{2} \frac{\left(v-v_0\right)}{a} $

- $ x  =\frac{v^2-v_0^2}{2 a} $

- $ v^2  =v_0^2+2 a x$.

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### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Acceleration </primary>
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- $a=\frac{v-v_0}{t} $

- $ v=v_0+a t $

- $\frac{1}{2}(v-v_0) t $

- displacement

- Area under $ {v-t}$ curve

- Area $=v_0 t+\frac{1}{2}\left(v- v_0\right) t $

-  displacement
 
 - $=v_0 t+\frac{1}{2} a t^2$.

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### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Acceleration </primary>
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- $ x  =v_0 t+\frac{1}{2} a t^2 $

- $ x  =\left(\frac{v+v_0}{2}\right) t$

- $ x  =\frac{\left(v+v_0\right)}{2} \frac{\left(v-v_0\right)}{a} $

- $ x  =\frac{v^2-v_0^2}{2 a} $

- $ v^2  =v_0^2+2 a x$.

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### <Success style="font-size:25px"> Frame Of Reference Motion In A Straight Line Uniform L-1 </Success>
### <primary style="font-size:24px"> Uniform Acceleration </primary>
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- $ v=v_0 + a t $ $\longrightarrow(x - x_0)$ missing

- $x=v_0 t+\frac{1}{2} a t^2 $ $\longrightarrow v $ missing

- $ v^2=v_b^2+2 a x $ $\longrightarrow t $ missing

- Valid only if $a=$ constant

- $x \rightarrow$ displacement

- $x_0 \neq 0$

- In above formulae  $x_0=0$.

- If $x_0 \neq 0 \rightarrow x$ replaced by $(x-x_0)$.

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