Question

Derive v=u+at
By calculus method?

Answer 1

See the picture for full description.

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

As we know that :

$\Huge{\underline{\boxed{\sf{a \: = \: \dfrac{dv}{dt}}}}}$

$\Large\leadsto {\sf{adv \: = \: dt}}$

Integrate both the sides

$\Large \leadsto {\sf{\displaystyle \int ^v_u \: dv \: = \: a\int ^t_0 \: dt}}$

$\Large\leadsto {\sf{\displaystyle \bigg[dv \bigg]^v _u \: = \: a \bigg[ dt \bigg]^t _0}}$

$\Large\leadsto {\sf{[v \: - \: u] \: = \: a[t \: - \: 0]}}$

$\LARGE : \implies {\boxed{\sf{v \: = \: u \: + \: at}}}$