Question

A body moves in a straight line along $Y-$axis. Its distance $y$ (in metre) from the origin is given by $y=8t-3t^2$ ($t$ in seconds). The average speed in the time interval from $t=0$ second to $t=2$ second is

• A. $1$ms${}^{-1}$
• B. $zero$
• C. $2$ms${}^{-1}$
• D. $\frac{22}{3}$ms${}^{-1}$

Answer 1

The correct option is D $\frac{22}{3}$ms${}^{-1}$

$v=\frac{dy}{dt}=8-6t$
Velocity becomes zero at $t=\frac{4}{3}$
$TotalDistancetravelledbyobject:betweent=0tot=\frac{4}{3}seconds\Rightarrow d=\frac{16}{3}m\therefore Totaldistancetravelledbetweent=0tot=2secondsis\Rightarrow 4+(2\times \frac{16}{3})=4+\frac{32}{3}=\frac{44}{3}m\Rightarrow Averagespeed=\frac{44}{3\times 2}=\frac{22}{3}$