Final answer:
The magnitude of the instantaneous velocity at 3.00 s, for the position function x(t) = 3.0t – 3t² m, is 15.0 m/s.
Step-by-step explanation:
To find the magnitude of the instantaneous velocity at 3.00 seconds (s), we need the velocity function resulting from the derivation of the position function x(t). For the given function x(t) = 3.0t – 3t² m, we can find the velocity function by taking the derivative with respect to time:
v(t) = dx/dt = d/dt (3.0t – 3t²) = 3.0 – 6t.
Now, substituting t = 3.00 s into this velocity function, we get:
v(3.00 s) = 3.0 – 6(3.00) = 3.0 – 18.0 = –15.0 m/s.
Note that the negative sign indicates the direction of the velocity vector, which is opposite to the positive direction intuitively defined in this context. However, the magnitude of this velocity, which is the absolute value, is 15.0 m/s.