Question

The position $x$ of a moving particle at time $t$ is given by $x=t^2+2t+3\text{m}$. The average velocity of the particle during the $t$ second of its motion is

• A. $(t+2){\text{ms}}^{-1}$
• B. $(t-2){\text{ms}}^{-1}$
• C. $t+2+\frac{3}{t}{\text{ms}}^{-1}$
• D. $3{\text{ms}}^{-1}$

Answer 1

The correct option is A $(t+2){\text{ms}}^{-1}$

$V_{\text{avg}}=\frac{\text{Displacement}}{\text{Time}}$
Displacement = Change in position = $x_t-x_0$
At $t=0s$, $x_0=0^2+2\times 0+3=3\text{m}$
and at $t=tsec$ , $x_t=(t^2+2t+3)\text{m}$
$V_{\text{avg}}=\frac{(t^2+2t+3)-3}{t}=\frac{t(t+2)}{t}=(t+2){\text{ms}}^{-1}$