Thank you for the opportunity to help you with your question!

S(t)=t^2 + 5t +3

instantaneous velocity is the derivative of the position with time,

v(t)=lim of delta t approaching zero((change in S(t)/change in time))=dS(t)/dt

v(t)=dS(t)/dt=2t +5

V(t)=2t +5

For every t, there is a different velocity at that given instant t, thus called instantaneous velocity .

Thus at instant t=1 second

V(1)=2x1+5=2+5=7 units/second and is directed along a straight line

V(1)=7 units/second i, where i denote the unit vector along the straight line of direction of motion. Remember velocity is a vector and must have not only magnitude but direction as well.

Please let me know if you need any clarification. I'm always happy to answer your questions.

Sep 11th, 2015

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