Question

The velocity of a particle is $v=v_0+gt+f{t}^2$. If its postion is $x=0$ at $t=0$, then its displacement after unit time $(t=1)$ is

• A. $v_0+\frac{g}{2}+f$
• B. $v_0+2g+3f$
• C. $v_0+\frac{g}{2}+\frac{f}{3}$
• D. $v_0+g+f$

Answer 1

Answer: (C)

$v_0+\frac{g}{2}+\frac{f}{3}$

$v=v_0+gt+f{t}^2$
$s=\int vdt$ $=\int (v_0+gt+f{t}^2)dt$

$=v_{0}t+g\frac{t^2}{2}+f\frac{t^3}{3}+c$

Given: $s_{t=0}=0$
$\Rightarrow c=0$
$\Rightarrow s_{t=1}=v_0+\frac{g}{2}+\frac{f}{3}$