Q. The initial velocity of a particle is $u\ (at\ t = 0)$ and the acceleration $f$ is given by $at$. Which of the following relation is valid
A) $v = u + at^{2}$
B) $v = u + a\frac{t^{2}}{2}$
C) $v = u + at$
D) $v = u$
Explanation
(b) If acceleration is variable (depends on time) then
$v = u + \ \int_{}^{}{(f)dt = u + \ \int_{}^{}\begin{array}{r}
(a\ t)dt = u + \frac{a\ t^{2}}{2} \\
\
\end{array}\ }$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.