physics-class-11-unit-03-chapter-03-motion-in-a-straight-line-lecture-3-3-qhvkp59ynee

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Problem </primary>
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- **A ball is dropped from the roof of a building with zero initial velocity. An the observer stands in front of a $100 \mathrm{~ cm}$ high window observes that the ball takes $0.2 \mathrm{~ s}$ to fall from top to bottom of a window. Then it touches the ground is later. Find the height of the building. Assume $g=10 \mathrm{~m} / \mathrm{s}^2$.**

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<footer style = "font-size: 18px">Motion in a Straight line $\rightarrow$ Motion in a straight line $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Solution $\rightarrow$ Solution </footer>

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Solution </primary>
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- $\downarrow x $

- $ a = + 9$

- $ = 10\text {m}/\text {s}^2$

- $ + = 0.2$

- $\left(x-x_0\right)=V_0 t+\frac{1}{2} a t^2$

- Use this formula from $1$ to $2$

- $1 m=V_1(0.2)+\frac{1}{2} g \times(0.2)^2$

- $\hspace {1cm} \uparrow \hspace {1.4cm} \uparrow 10$

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<footer style = "font-size: 18px">Motion in a straight line $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Solution </span> $\rightarrow$ Solution $\rightarrow$ Solution </footer>

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Solution </primary>
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- $\downarrow x $

- $ a = + 9$

- $ = 10\text {m}/\text {s}^2$

- $ + = 0.2$

- $\left(x-x_0\right)=V_0 t+\frac{1}{2} a t^2$

- use this formula from $1$ to $2$

- $1 m=V_1(0.2)+\frac{1}{2} g \times(0.2)^2$

- $\hspace {1cm} \uparrow \hspace {1.4cm} \uparrow 10$

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

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Problem </primary>
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- **A train travels from station $A$ to station $B$. It starts from rest at $A$, undergoes constant acceleration $a_1$ in its first part of motion and then undergoes constant retardation $a_2$ till it comes to rest. Find the total time of the journey in terms of $a_1, a_2$ and $l$, the distance between $A ~ \\& ~ B$.**

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

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Solution </primary>
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- $\left.\begin{array}{l} A C=S_1 \\\\ C B=S_2 \end{array}\right\\} \quad S_1+S_2=l$

- $\text { Let velocity at } C \text { be } V_C$

- $V_C^2=V_A^2+2 a_1 s_1 \rightarrow S_1 = \frac{V_C^2}{2a_1}$

- $ V_B^2=V_C^2-2 a_2 s_2\rightarrow S_2 = \frac{V_C^2}{2a_2}$

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

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Problem </primary>
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<footer style = "font-size: 18px">Solution $\rightarrow$ Method-2 Graphical method $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Solution $\rightarrow$ Solution </footer>

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Solution </primary>
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- $ t_1=\frac{v_c}{a_1} $

- $ t_2=\frac{v_c}{a_2} $

- $\left(t_1+t_2\right)=\frac{v_c}{a_1}+\frac{v_c}{a_2}=v_c\left(\frac{1}{a_1}+\frac{1}{a_2}\right)$

- $v_c=\frac{l}{2 t} \Rightarrow t_2 $

- $ t=\frac{l}{2 t}\left(\frac{1}{a_1}+\frac{1}{a_2}\right) $

- $\Rightarrow t^2 = \frac{l}{2} \left(\frac{1}{a_1}+\frac{1}{a_2}\right)$

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<footer style = "font-size: 18px">Problem $\rightarrow$ Solution $\rightarrow$ <span style = "color:blue"> Solution </span> $\rightarrow$ Solution $\rightarrow$ Relative Velocity and Acceleration </footer>

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Solution </primary>
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- $\text { Find } t_1 \text { to } t_2:$

- $\left(t_1+t_2\right)=\frac{v_c}{a_1}+\frac{v_c}{a_2}=v_c\left(\frac{1}{a_1}+\frac{1}{a_2}\right)$

- $v_c=\frac{l}{2 t} \Rightarrow t_2 $

- $ t=\frac{l}{2 t}\left(\frac{1}{a_1}+\frac{1}{a_2}\right) $

- $\Rightarrow t^2 = \frac{l}{2} \left(\frac{1}{a_1}+\frac{1}{a_2}\right)$

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

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Relative Velocity </primary>
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- **Let us consider a point $P$ moving in a straight line**.

- **An observer attached to frame $A$**

- **$x_{\text {PA}}$ location of $P$ as observed by observer attached to frame $A$.**

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

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Relative Velocity </primary>
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- $ x_{P A}=x_{P B}+x_{B A}$

- $ \frac{d x_{P A}}{d t}=\frac{d x_{P B}}{d t}+\frac{d x_{B A}}{d t} $

- $v_{P A}=\hspace {0.1cm}v_{P B}\hspace {0.1cm}+v_{B A}$

- $v_{P A} \rightarrow  \text { Velocity of } P \text { as observed from frame } A$

- $v_{P B} \rightarrow\text { Velocity of } P \text { as observed from frame } B$

- $v_{B A} \rightarrow\text { Velocity of } B \text { as observed from frame }A$

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

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Relative Velocity </primary>
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- $A \rightarrow \text{ Fixed to ground } $

- $A \text { may be dropped. }$

- $v_P = v_{PB} + v_B$

- $v_{PB} = v_P - v_B$

- $v_{PB} \rightarrow \text { Velocity of }P \text { as observed by frame } B$

- $v_P \rightarrow \text { Velocity of } P$

- $v_B \rightarrow \text { Velocity of } B$

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

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Relative Velocity in Escalator </primary>
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- **Person walks up a stalled escalator in time $t_1$. On a moving escalator a person at rest wr.t. escalator moves up in $t_2$.**

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

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Relative Velocity in Escalator </primary>
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- **Time in which the person will move from bottom to top of escalator if he moves up both his speed $C$  ecalator is also moving.**

- Person $P: \hspace {0.5cm} v_p=\frac{l}{t_1}$

- Escalator moves $\rightarrow v_P = $ Velocity of person

- w.r.t. Escalator

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<footer style = "font-size: 18px">Relative Velocity $\rightarrow$ Relative Velocity in Escalator $\rightarrow$ <span style = "color:blue"> Relative Velocity in Escalator </span> $\rightarrow$ Relative Velocity in Escalator $\rightarrow$ Relative Velocity in Escalator </footer>

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Relative Velocity in Escalator </primary>
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- $\text { Person moves up stopped } \rightarrow t_1 \text { escalator, }$

- $\text { Bottom to top } \rightarrow t_2$

- $\text { Person moves with his speed on moving escalator} \rightarrow  \text { find } t_3$.

- $\text { Length of the escalator } =l$

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<footer style = "font-size: 18px">Relative Velocity in Escalator $\rightarrow$ Relative Velocity in Escalator $\rightarrow$ <span style = "color:blue"> Relative Velocity in Escalator </span> $\rightarrow$ Relative Velocity in Escalator $\rightarrow$ Problem </footer>

### <Success style="font-size:25px"> Motion In A Straight Line L-3 </Success>
### <primary style="font-size:24px"> Problem </primary>
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- **Two towns $A$ and $B$ are connected by $a$ bus service with bus leaving in either direction in $T$ minutes $A$ man  cycling at $20 \mathrm{~ km} / \mathrm{h}$ in direction from $A$ to $B$ observes a bus going post him every 18 minutes in direction of motion and every 6 minutes in opposite direction. Assuming bus speed $V_B=$ constant, find $V_B$ and $T$.**

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<footer style = "font-size: 18px">Relative Velocity in Escalator $\rightarrow$ Relative Velocity in Escalator $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Solution $\rightarrow$ Solution </footer>