Question

ɢᴏᴏᴅ ᴍᴏʀɴɪɴɢ ᴇᴠᴇʀʏᴏɴᴇ
ᴀɴsᴡᴇʀ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ᴡɪᴛʜ ғᴜʟʟ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ
sᴘᴀᴍ ᴡɪʟʟ ʙᴇ ʀᴇᴘᴏʀᴛᴇᴅ
ᴅᴏɴ'ᴛ ᴄᴏᴘʏ ғʀᴏᴍ ɢᴏᴏɢʟᴇ​

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept\;:-}}}$

Here the Concept of Distance and Time Relationship has been used . We see that we are given the speed of scooter of Ajit . Now its given a of one hour abd its also said that speed is constant . We also see that we need to find the speed till 3½ hours . So we need to plot the graph for 4 hours and then find the things .

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{\pink{Distance\;=\;\bf{Speed\:\times\:Time}}}}$

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★ Solution :-

Given,

» Speed of the Ajit's scooter = 30 Km/Hr

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~ For Graph ::

We see that we are given that constant speed that is 30 Km/hr . Then this means distance covered in 1 hour is 30 Km .

Then,

$\\\;\sf{:\rightarrow\;\;Distance\;=\;\bf{Speed\:\times\:Time}}$

• Distance covered in 2 hours ::

$\\\;\sf{:\Longrightarrow\;\;Distance_{(2\:hr)}\;=\;2\:\times\:30\;=\;\bf{\underline{\green{60\;\:Km\:hr^{-1}}}}}$

• Distance covered in 3 hours ::

$\\\;\sf{:\Longrightarrow\;\;Distance_{(3\:hr)}\;=\;3\:\times\:30\;=\;\bf{\underline{\green{90\;\:Km\:hr^{-1}}}}}$

• Distance covered in 4 hours ::

$\\\;\sf{:\Longrightarrow\;\;Distance_{(4\:hr)}\;=\;4\:\times\:30\;=\;\bf{\underline{\green{120\;\:Km\:hr^{-1}}}}}$

From this we can see that :

• Time = 1 hour, Distance = 30 Km

• Time = 2 hour, Distance = 60 Km

• Time = 3 hour, Distance = 90 Km

• Time = 4 hour, Distance = 120 Km

Using this we can plot the graph. This is shown in the attachment .

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i) Time Taken by Ajit to ride 75 Km ::

From graph we see that, the line for Distance - Time graph is straight this mean speed is constant . This also means the Time will correspond to the position . From graph we get the time to be 2.5 hours .

This can be proved as ::

$\\\;\sf{:\rightarrow\;\;Distance\;=\;\bf{Speed\:\times\:Time}}$

$\\\;\sf{:\Longrightarrow\;\;75\;=\;\bf{30\:\times\:Time}}$

$\\\;\sf{:\Longrightarrow\;\;Time\;=\;\bf{\dfrac{75}{30}}}$

$\\\;\bf{:\Longrightarrow\;\;Time\;=\;\bf{2.5\;\:hr}}$

$\\\;\underline{\boxed{\tt{Hence,\;\;Time\;\;Taken\;=\;\bf{\purple{2.5\;\;hr}}}}}$

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~ Distance covered by Ajit in 3½ Hours ::

We see the to find the distance covered we need to find the point which corresponds to the Distance Axis . We find that point as 105 Km which satisfies condition as it lies on the line proving the condition of constant speed.

This can be proved as ::

3½ hours = 3.5 hours

And,

$\\\;\sf{:\rightarrow\;\;Distance\;=\;\bf{Speed\:\times\:Time}}$

$\\\;\sf{:\Longrightarrow\;\;Distance\;=\;\bf{30\:\times\:3.5}}$

$\\\;\bf{:\Longrightarrow\;\;Distance\;=\;\bf{105\;\:Km}}$

$\\\;\underline{\boxed{\tt{Hence,\;\;Distance\;\;Covered\;=\;\bf{\orange{105\;\;Km}}}}}$

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★ More to know :-

$\\\;\sf{\gray{\leadsto\;\;Acceleration\;=\;\dfrac{(v\;-\;u)}{t}}}$

$\\\;\sf{\gray{\leadsto\;\;s\;=\;ut\;+\;\dfrac{1}{2}\:at^{2}}}$

$\\\;\sf{\gray{\leadsto\;\;v^{2}\;-\;u^{2}\;=\;2as}}$

$\\\;\sf{\gray{\leadsto\;\;Velocity\;=\;\dfrac{Displacement}{Time}}}$

$\\\;\sf{\gray{\leadsto\;\;s_{n_{th}}\;=\;u\;+\;\dfrac{a}{2}\:(2n\;-\;1)}}$

Answer 2

$❥{\huge{\underline{\small{\mathbb{\pink{YOUR \ CORRECT \ ANSWER }}}}}}$

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