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) \[5m{{s}^{-1}},14m{{s}^{-2}}\]
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 \[\therefore \] \[v=\frac{dy}{dt}=5+14\,t\] Initial velocity at \[t=0,\]is \[v=5\,m/s.\] Also acceleration \[a=\frac{{{d}^{2}}y}{d{{t}^{2}}}=14\,m/{{s}^{2}}\]
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