A) \[14m{{s}^{-1}},\,\,5\,\,m{{s}^{-2}}\]
B) \[19m{{s}^{-1}},\,\,-9m{{s}^{-2}}\]
C) \[-14m{{s}^{-1}},\,\,-5m{{s}^{-2}}\]
D) \[5m{{s}^{-1}},\,\,14\,\,m{{s}^{-2}}\]
Correct Answer: D
Solution :
Key Idea: 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 \[\therefore \] \[v=\frac{dy}{dt}=5+14t\] Initial velocity at\[t=0\], is \[v=5\,\,m/s\] Also acceleration\[a=\frac{{{d}^{2}}y}{d{{x}^{2}}}=14\,\,m/{{s}^{2}}\]
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