This question tests AP Physics C kinematics, specifically understanding velocity components in projectile motion under uniform gravity. The motion in two dimensions requires recognizing that gravity acts only vertically, leaving horizontal motion unaffected. In this scenario with no air resistance, only gravity acts on the projectile, providing constant downward acceleration. Choice B is correct because vₓ remains constant (no horizontal forces) while vᵧ decreases linearly due to constant gravitational acceleration (vᵧ = v₀ᵧ - gt). Choice A reverses the components, C incorrectly suggests both components change, and D misunderstands that while speed changes, velocity components change predictably. To help students: Emphasize the independence of horizontal and vertical motion in projectile problems. Practice analyzing force diagrams to identify which components experience acceleration. Watch for: confusing speed with velocity or forgetting that only vertical motion is affected by gravity.

This question tests AP Physics C kinematics, specifically centripetal acceleration in circular motion. The motion in two dimensions for uniform circular motion requires understanding that acceleration always points toward the center of the circular path. In this scenario, a car travels on a 50 m radius track at constant speed 12 m/s, requiring centripetal acceleration a = v²/r. Choice B is correct because a = (12)²/50 = 144/50 = 2.88 m/s² directed inward toward the center. Choice A incorrectly states the direction as outward, violating Newton's laws for circular motion. Choices C and D show incorrect calculations of the acceleration magnitude. To help students: Emphasize that centripetal acceleration always points toward the center, regardless of the direction of motion. Practice identifying the radius and speed in various circular motion scenarios. Watch for: confusion between centripetal and centrifugal effects, or errors in applying the v²/r formula.

This question tests AP Physics C kinematics, specifically centripetal acceleration in uniform circular motion. The motion in two dimensions requires understanding that objects in circular paths experience constant inward acceleration even at constant speed. In this scenario, an object moves at v = 20 m/s on a circular path of radius 80 m, requiring centripetal acceleration. Choice C is correct because a = v²/r = (20)²/80 = 400/80 = 5.0 m/s² directed radially inward toward the center. Choices A incorrectly identifies the direction as tangential, while B and D show incorrect calculations of the magnitude. To help students: Emphasize the distinction between tangential acceleration (changes speed) and centripetal acceleration (changes direction). Practice calculating v²/r for various circular motion scenarios. Watch for: confusion between radial and tangential directions, or arithmetic errors in the v²/r calculation.

This question tests AP Physics C kinematics, specifically motion on inclined planes in two dimensions. The motion requires decomposing gravitational acceleration into components parallel and perpendicular to the incline surface. In this scenario, a block slides down a frictionless 30° incline, experiencing only the component of gravity parallel to the surface. Choice B is correct because a_parallel = g·sin(30°) = 9.8 × 0.5 = 4.9 m/s² down the incline. Choice A incorrectly uses the full gravitational acceleration, C and D show wrong magnitudes or directions. To help students: Practice decomposing weight into components using free body diagrams on inclines. Emphasize that on frictionless surfaces, only the parallel component of weight causes acceleration. Watch for: using cosine instead of sine, or confusing the direction of acceleration with the normal force direction.

This question tests AP Physics C kinematics, specifically motion in two or three dimensions for uniform circular motion velocity vectors. The motion requires understanding how velocity vectors behave in circular motion - constant magnitude but continuously changing direction. In this scenario, we analyze how the velocity vector evolves during uniform circular motion. Choice A is correct because it accurately describes that velocity magnitude stays constant while direction rotates, and the change in velocity (Δv) points inward toward the center, creating centripetal acceleration. Choice C is incorrect because it suggests the velocity vector doesn't change at all, which would mean no acceleration and thus no circular motion. To help students: Use vector diagrams showing velocity at different points around the circle. Demonstrate how subtracting consecutive velocity vectors yields an inward-pointing Δv. Watch for: confusion between speed (scalar) and velocity (vector) and misunderstanding how vector subtraction works.