Let's break down the problem step by step: --- ### **Step 1: Understanding the Motion** - **Given:** - The bracket A is traveling at a velocity \( v_A = 3 \) m/s to the right on the smooth slot. - The slot is moving upward at \( v_{slot} = 0.5 \) m/s. - The bracket is moving up the straight-away and increasing its speed at \( a_A = 2 \) m/s². - **Task:** - Find the relative acceleration of A with respect to B of the slot. **Explanation:** Here, we need to find the acceleration of bracket A relative to the slot B. Since both are moving, we use the relative acceleration formula: \[ \vec{a}_{A/B} = \vec{a}_A - \vec{a}_B \] where \(\vec{a}_A\) is the acceleration of A and \(\vec{a}_B\) is the acceleration of the slot (B). --- ### **Step 2: Calculating Acceleration Components** - **Slot B (moving vertically):** - Given only velocity, not acceleration, so \( a_B = 0 \) (since the velocity is constant). - **Bracket A:** - It is increasing its speed at \( 2 \) m/s² (along the straight path, assumed horizontal). - The direction of motion is horizontal (right). So, \[ \vec{a}_A = 2 \hat{i} \text{ m/s}^2 \] \[ \vec{a}_B = 0 \text{ m/s}^2 \] \[ \vec{a}_{A/B} = 2 \hat{i} - 0 = 2 \hat{i} \text{ m/s}^2 \] **Explanation:** Since the slot moves with constant velocity upward, its acceleration is zero. All the acceleration is due to A's motion, which is along the horizontal. The relative acceleration is therefore just A's acceleration in the horizontal direction. --- ## **Final Answer:** **The relative acceleration of A with respect to B is \( 2 \) m/s² to the right (horizontal direction).**