Question

Derive the first equation of kinematics​

Answer 1

$\mapsto\bf{first \:equation\: of \:kinematics}$

➦$\begin{gathered}a=\dfrac {v-u}{t-0}\\\\\\v-u=at\\\\\\\boxed {v=u+at}\end{gathered}$

➦ $\begin{gathered}\displaystyle s=\int\limits_{0}^{t}v\ dt\\\\\\s=\int\limits_{0}^{t}(u+at)\ dt\\\\\\s=\int\limits_{0}^{t}u\ dt+\int\limits_{0}^{t}at\ dt\\\\\\s=u\left [t\right]_0^t+a\left [\dfrac {t^2}{2}\right]_0^t\\\\\\\boxed {s=ut+\dfrac {1}{2}at^2}\end{gathered}$

Done :)

Thankyou :)

Answer 2

ᴛʜɪꜱ ɢɪᴠᴇꜱ ᴜꜱ ᴛʜᴇ ᴠᴇʟᴏᴄɪᴛʏ-ᴛɪᴍᴇ ᴇQᴜᴀᴛɪᴏɴ. ɪꜰ ᴡᴇ ᴀꜱꜱᴜᴍᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪꜱ ᴄᴏɴꜱᴛᴀɴᴛ, ᴡᴇ ɢᴇᴛ ᴛʜᴇ ꜱᴏ-ᴄᴀʟʟᴇᴅ ꜰɪʀꜱᴛ ᴇQᴜᴀᴛɪᴏɴ ᴏꜰ ᴍᴏᴛɪᴏɴ . ᴀɢᴀɪɴ ʙʏ ᴅᴇꜰɪɴɪᴛɪᴏɴ, ᴠᴇʟᴏᴄɪᴛʏ ɪꜱ ᴛʜᴇ ꜰɪʀꜱᴛ ᴅᴇʀɪᴠᴀᴛɪᴠᴇ ᴏꜰ ᴘᴏꜱɪᴛɪᴏɴ ᴡɪᴛʜ ʀᴇꜱᴘᴇᴄᴛ ᴛᴏ ᴛɪᴍᴇ.

...

ᴄᴏɴꜱᴛᴀɴᴛ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ.

ᴠ = ᴠ0 + ᴀᴛ [1]

+

ꜱ = ꜱ0 + ᴠ0ᴛ + ½ᴀᴛ2 [2]

=

ᴠ2 = ᴠ02 + 2ᴀ(ꜱ − ꜱ0) [3]