The motion of a particle is described by the equation $x=a t+b t^2$, where $a=15 \mathrm{~cm} \mathr

Question

The motion of a particle is described by the equation $x=a t+b t^2$, where $a=15 \mathrm{~cm} \mathrm{~s}^{-1}$ and $b=3 \mathrm{~cm} \mathrm{~s}^{-2}$. Its instantaneous velocity (in $\mathrm{cm} \mathrm{s}^{-1}$ ) at $t=3 \mathrm{~s}$ will be

Professor PC Thomas Classes · Answer

(a): Here, $x=a t+b t^2$\ where $a=15 \mathrm{~cm} \mathrm{~s}^{-1}, b=3 \mathrm{~cm} \mathrm{~s}^{-2}$\ Velocity, $v=\frac{d x}{d t}=\frac{d}{d t}\left(a t+b t^2ight)=a+2 b t$\ At $t=3 \mathrm{~s}, v=15+2 	imes 3 	imes 3=33 \mathrm{~cm} \mathrm{~s}^{-1}$