The position of an object moving along $x$-axis is given by $x=a+b t^2$, where $a=8.5 \mathrm{~m}$ a

Question

The position of an object moving along $x$-axis is given by $x=a+b t^2$, where $a=8.5 \mathrm{~m}$ and $b=2.5 \mathrm{~m} \mathrm{~s}^{-2}$ and $t$ is measured in seconds. The instantaneous velocity (in $\mathrm{m} \mathrm{s}^{-1}$ ) of the object at $t=2 \mathrm{~s}$ is

Professor PC Thomas Classes · Answer

(b): Here, $x=a+b t^2$\ Where, $a=8.5 \mathrm{~m}$ and $b=2.5 \mathrm{~m} \mathrm{~s}^{-2}$\ Velocity, $v=\frac{d x}{d t}=\frac{d}{d t}\left(a+b t^2ight)=2 b t$\ At $t=2 \mathrm{~s}, v=2\left(2.5 \mathrm{~m} \mathrm{~s}^{-2}ight)(2 \mathrm{~s})=10 \mathrm{~m} \mathrm{~s}^{-1}$