Question

If $S=ut+\frac{1}{2}a{t}^2$, where $S$ is displacement, $u$ is initial velocity (constant), $a$ is acceleration (constant) and $t$ is time taken, then differentiation of $S$ w.r.t. $t$ 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 $u+at$

$S=ut+1/2a{t}^2$

$\frac{dS}{dt}=u+\frac{1}{2}\times a\times 2t=u+at$

(This is the velocity of particle at any time $t$)