Identify the velocity function and check for changes in direction.

Step 1: Identify the velocity function and check for changes in direction. The velocity of the particle is given by v = (-2t + 4) m/s. To determine if the particle changes direction within the first second (t=0 to t=1), we find when v = 0. -2t + 4 = 0 2t = 4 t = 2 s Since t = 2 s is outside the interval [0, 1] s, the particle does not change direction during the first second. Therefore, the distance moved is simply the absolute displacement. Step 2: Find the position function. Position s is the integral of velocity with respect to time t. s = v \, dt = (-2t + 4) \, dt s = -t^2 + 4t + C For calculating the distance moved, we can assume the initial position at t=0 is s=0. 0 = -(0)^2 + 4(0) + C C = 0 So, the position function is: s(t) = -t^2 + 4t Step 3: Calculate the distance moved during the first second. The distance moved is the absolute difference between the position at t=1 and the position at t=0. s(1) = -(1)^2 + 4(1) = -1 + 4 = 3 m s(0) = -(0)^2 + 4(0) = 0 m Distance moved = |s(1) - s(0)| = |3 - 0| = 3 m. The distance moved by the particle during the first second of its motion is 3 m. That's 2 down. 3 left today — send the next one.