Question

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

• A. $33\,cm\, s^{-1}$
• B. $18\,cm\, s^{-1}$
• C. $16\,cm\, s^{-1}$
• D. $32\,cm\, s^{-1}$

Answer 1

Answer: (A)

Here, $x = at + bt^2$
where $a = 15 \,cm\, s^{-1}$, $b = 3 \,cm \,s^{-2}$
Velocity, $v=\frac{dx}{dt}=\frac{d}{dt}\left(a+bt^{2}\right)=a+2bt$
At $t = 3\,s$, $v = 15+ 2 \times 3 \times 3$
$ = 33 \,cm \,s^{-1}$