Question

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

Answer 1

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)

Answer 2

s(t) = 4at^2 + 7
 s'(t) = v =  8at

so velocity at t = 4 =  8a*4 = 32a