Question

Q. speed of a body moving with uniform acceleration is u. Speed is doubled while covering
a distance S. Find its speed when it covers an additional distance S.


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Answer 1

✪ᴀɴsᴡᴇʀ✪

• Speed of the body after covering additional distance S is $\sqrt{7}u$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

☆ɢɪᴠᴇɴ☆

• A body under uniform acceleration is moving with speed u at an instant.

• The speed becomes 2u after covering distance S.

☆ᴛᴏ ғɪɴᴅ☆

• Speed of the body after covering another distance S.

᯽ғᴏʀᴜᴍʟᴀ᯽

• For a body in uniform motion,

$\:\:\:\:\:\:\:\:\:\boxed{ v^2 - u^2 = 2aS}$

☆ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ☆

After covering distance S, speed becomes double, so

$\:\:\:\:\: v = 2u$

Using this in the above equation, we get

$\:\:\:\:\: (2u)^2 - u^2 = 2aS$

$\to 4u^2 - u^2 = 2aS$

$\to 3u^2 = 2aS$

$\to a = \frac{3u^2}{2S}$

Let v be the speed after coveing another distance S. Applying the above formula and using the value of 'a', we get

$\:\:\:\:\: v^2 - (2u)^2 = 2\left(\frac{3u^2}{2S}\right)S$

$\to v^2 - 4u^2 = 3u^2$

$\to v^2 = 4u^2 + 3u^2$

$\to v^2 = 7u^2$

$\to v = \sqrt{7}u$