Suppose the position of an object moving in a straight line is given by
s(t)=t squared+5t+3. Find the instantaneous velocity when t=1.
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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
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.
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