Question

The acceleration of a particle, starting from rest, varies with time according to the relation a = Kt + C, where K and C are constants of motion. The velocity ‘V’ of the particle after a time ‘t’ will be

• A. $Kt+Ct$
• B. $\frac{1}{2}K{t}^2+Ct$
• C. $\frac{1}{2}(K{t}^2+Ct)$
• D. $K{t}^2+\frac{1}{2}Ct$

Answer 1

The correct option is B $\frac{1}{2}K{t}^2+Ct$

$a=Kt+c\frac{dv}{dt}=Kt+c\Rightarrow dv=(Kt+c)dt\Rightarrow \int dv=\int Ktdt+\int cdt\Rightarrow v=\frac{K{t}^2}{2}+ct$