Final answer:
The velocity function v(t) for the object with position function x(t) = -3t² m is the derivative of the position with respect to time, resulting in v(t) = -6t m/s. At 1.0 s, the velocity is -6 m/s and the speed is 6 m/s. The velocity is never positive as it is always moving in the negative direction.
Step-by-step explanation:
The velocity of the object as a function of time is given by the derivative of the position function x(t). So, for the position function x(t) = -3t² m, the velocity function v(t) is found by differentiating x(t) with respect to t, giving us v(t) = -6t m/s. This velocity function tells us the rate of change of the object's position with respect to time. The speed of the object, which is the magnitude of the velocity, is simply |v(t)|.
At time t = 1.0 s, the velocity is v(1.0 s) = -6 m/s and the speed is |v(1.0 s)| = 6 m/s. The negative sign indicates the direction of the velocity vector. The velocity is never positive since the derivative is -6t, which for all positive values of t will be negative, meaning the object is always moving in the negative direction.