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

The Correct Option is D

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}} $