1. The figure shows two possible paths for negotiating an unbanked turn on a horizontal portion of a race course. Path A-A follows the centerline of the road and has a radius of curvature Ρ_A = 85 m, while path B-B uses the width of the road to good advantage in increasing the radius of curvature to Ρ_B= 200 m. If the drivers limit their speeds in their curves so that the lateral acceleration does not exceed 0.8g, determine the maximum speed for each path.

2. In the design of a timing mechanism, the motion of the pin A in the fixed circular slot is controlled by the guide B, which is being elevated by its lead screw with a constant upward velocity v_o = 2 m/s for an interval of its motion. Calculate both the normal and tangential components of acceleration of pin A as it passes the position for which θ = 30°.

3. The design of a camshaft-drive system of a four-cylinder automobile engine is shown. As the engine is revved up, the belt speed v changes uniformly from 3 m/s to 6 m/s over a two-second interval. Calculate the magnitudes of the accelerations of points P₁ and P₂ halfway through this time interval.

4. The ladder of a fire truck is designed to be extended at the constant rate i = 6 in./sec and to be elevated at the constant rate θ = 2 deg/sec. As the position θ = 50° and l= 15 ft is reached, determine the mag-nitudes of the velocity v and the acceleration a of the fireman at A.