Suppose an object moves along a line with velocity (in \( \mathrm{ft} / \mathrm{s} \) ) \( v(\mathrm{t})=6-4 \mathrm{t} \), for \( 0 \leq t \leq 3 \), where t is measured in seconds. The motion is in the positive direction on the interval \( [0,1.5) \) : (Type your answer in interval notation.) The motion is in the negative direction on the interval \( \square \). (Type your answer in interval notation.)

To determine when the object is moving in the negative direction, we start with the velocity function \( v(t) = 6 - 4t \). The object moves in the negative direction when \( v(t) < 0 \). Set \( v(t) < 0 \): \[ 6 - 4t < 0 \] Solving this inequality gives: \[ 6 < 4t \\ t > \frac{6}{4} \\ t > 1.5 \] Since the object is constrained within the interval \( [0,3] \), the motion will be in the negative direction on the interval \( (1.5, 3] \). Thus, the answer for the negative motion interval is \( (1.5, 3] \). In summary, the motion is in the positive direction on \( [0, 1.5) \) and in the negative direction on \( (1.5, 3] \).