Question

The position coordinates of a particle moving in $X-Y$ as a function of time $t$ are

$x=2t^2+6t+25$

$y=t^2+2t+1$

The speed of the object at $t=10s$ is approximately

• A. $31units$
• B. $51units$
• C. $71units$
• D. $81units$

Answer 1

Answer: (B)

Given, $x=2t^2+6t+25andy=t^2+2t+1$
$\therefore \frac{dx}{dt}=4t+6and\frac{dy}{dt}=2t+2$
$Att=10s$
$\frac{dx}{dt}=4\left(10\right)+6=46and\frac{dy}{dt}=2\left(10\right)+2=22$
$v=\sqrt{{\left(\frac{dx}{dt}\right)}^2+{\left(\frac{dy}{dt}\right)}^2}$
$=\sqrt{{\left(46\right)}^2+{\left(22\right)}^2}\simeq 51units$