The position of an object at time t is given by s(t). find the instantaneous velocity at the indicated value of t. s(t) = 4at^2 + 7 at t = 4

If the position is given by s(t) = 4at^2 + 7
(by which I assume you mean  s(t) = 4*a*t^2 + 7)

then the velocity is given by the derivative ds/dt, which is 4*a*2*t.

Now let t = 4:  (ds/dt)(4) = 4*a*2^4 = 4*a*16 = 64a (answer)

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