Question

If the displacement of particle at any time $t$ is given by $s=ut+\frac{1}{2}a{t}^2$ where $u$ is initial velocity (constant) and $a$ is acceleration (constant) then, velocity of particle at any time $t$ will be

• A. $u+\frac{at}{2}$
• B. $u+at$
• C. $u+2at$
• D. $\frac{u{t}^2}{2}+\frac{a{t}^3}{6}$

Answer 1

The correct option is B $u+at$

We know velocity is the first derivative of displacement, $v=\frac{ds}{dt}=u+\frac{1}{2}a\times 2t=u+at$