Question

A particle moves according to the equation $x=2t^2-5t+6$. Find (i) average velocity in the first $3\text{sec}$ and (ii) velocity at $t=3\text{s}$.

• A. $1{\text{ms}}^{-1},7{\text{ms}}^{-1}$
• B. $4{\text{ms}}^{-1},3{\text{ms}}^{-1}$
• C. $2{\text{ms}}^{-1},5{\text{ms}}^{-1}$
• D. $3{\text{ms}}^{-1},7{\text{ms}}^{-1}$

Answer 1

The correct option is A $1{\text{ms}}^{-1},7{\text{ms}}^{-1}$

$x\left(3\right)=2(3{)}^2-5(3)+6=9,x(0)=6$
$v_{av}=\frac{x\left(3\right)-x\left(0\right)}{3-0}=\frac{9-6}{3}=1{\text{ms}}^{-1}$
${\begin{array}{c}\frac{dx}{dt}\end{array}|}_{t=3}=4t-5=4\left(3\right)-5=7{\text{ms}}^{-1}$