Question

The initial velocity of a particle is $u$ $(att=0)$ and the acceleration is given by $f=at$. Which of the following relations is valid?

• A. $v=u+a{t}^2$
• B. $v=u+\frac{a{t}^2}{2}$
• C. $v=u+at$
• D. $v=u$

Answer 1

The correct option is B $v=u+\frac{a{t}^2}{2}$

As $f=at\Rightarrow \frac{dv}{dt}=at$

$\Rightarrow {\int }_u^{v}dv={\int }_0^{t}atdt\Rightarrow v-u=\frac{a{t}^2}{2}$

$\Rightarrow v=u+\frac{1}{2}a{t}^2$