Question

The acceleration of a particle starting from rest varies with time according to the relation $a=kt+c$. The velocity $v$ of the particle after time $t$ will be

• A. $k{t}^2+ct$
• B. $\frac{1}{2}(k{t}^2+ct)$
• C. $\frac{1}{2}(k{t}^2+4ct)$
• D. $\frac{k{t}^2}{2}+ct$

Answer 1

The correct option is D $\frac{k{t}^2}{2}+ct$

We know that
Acceleration, $a=\frac{dv}{dt}\Rightarrow v=\int adt={\int }_0^t(kt+c)dt\text{Velocity,}v=\frac{k{t}^2}{2}+ct$