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Q. Convert a light year to meter. ( step by step )

Q. The velocity-time graphs of two objects make angles of 30 degree and 60 degree with the time axis. Find the ratio of their acceleration. ( steps needed no direct answer please )

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Answer 1

Answer:

that is not the way u ask the question ..... u should be pleased to ask..any way say wether is it right or not

Answer 2

$\bf\small\bold{\underline{\underline{Step-By-Step\:Explanation:-}}}$

A. Light year is the time taken by light to travel in 1 year time.

We know the speed of light is $\bold\green{3 \times 10^8 m/s}$

That is It covers $\bold\green{3 \times10^8 m}$ in 1 second.

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

How many seconds in 1 year :

Now let us find how many seconds are there in 1 year.

$\longrightarrow \large \bold{1\:year=365\:days = 365 \times 24\:hours }$

$\longrightarrow \large \bold{ 1\:year=365\times24\times60 \:min}$

$\longrightarrow \large \bold{1\:year=365\times24\times60\times60 sec=31536000 sec}$

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Now light travels in 1 second = $\tt{3 \times 10^8 m}$

⇒Light travels in 31536000 seconds =$\tt{94608000\times\:10^8 m}$

$\longrightarrow \large \bold{1 light \:year = 9.46 \times\:10^{15} m }$

$\rule{200}{4}$

B. The acceleration is given as

a = dv/dt

Now in the v-t graph v is the y axis while t is the x-axis. So the above relation can also be written as trigonometric ratio where

dv/dt = tanθ

Here θ is the angle made by the v-t graph with the x-axis or the time axis.

So, acceleration will be, a = tanθ

Now,

✭for plot 1, θ = 30 degrees

so, ⇒a1 = tan30° = $\bf\bold{\frac{1}{\sqrt{3}}}$m/s²

and

✭for plot 2, θ = 60 degrees

⇒a2 = tan60° = $\bf\bold{\sqrt{3}}$m/s²

thus, the ration of accelerations will be

$\longrightarrow \large \bold{\frac{a_1}{a_2} =\frac{1}{\sqrt{3}\times\sqrt{3}} }$

Hence, the ratio is

$\longrightarrow \large \bold{\frac{a_1}{a_2} = \frac{1}{3} }$