Question

A particle moves along Y-axis in such a way that its $y-$ coordinate varies with time $t$ according to the relation $y=3+5t+7{{t}^{2}}.$ The initial velocity and acceleration of the particle are respectively:

• A. $14m{{s}^{-1}},-5\,m{{s}^{-2}}$
• B. $19\,m{{s}^{-1}},-9\,m{{s}^{-2}}$
• C. $-14\,m{{s}^{-1}},-5\,m{{s}^{-2}}$
• D. $5m{{s}^{-1}},14m{{s}^{-2}}$

Answer 1

Answer: (D)

$5m{{s}^{-1}},14m{{s}^{-2}}$

Answer 2

Rate of change of position is known as velocity and rate of change of velocity is known as acceleration.
Given $y=3+5t+7{{t}^{2}}$
Velocity $(v)$ is defined as rate of change of displacement, also using
$\frac{d}{dx}{{x}^{n}}=n{{x}^{n-1}},$
we have $\therefore$ $v=\frac{dy}{dt}=5+14\,t$
Initial velocity at $t=0,$ is $v=5\,m/s.$
Also acceleration $a=\frac{{{d}^{2}}y}{d{{t}^{2}}}=14\,m/{{s}^{2}}$