{"id": "physics-v1-K1-R3-48c8f309-a0", "prompt": "A person walks 800 m due east in a warehouse, then turns around and walks 350 m due west. What is the magnitude of the person's displacement?", "chosen": "The person walks 800 m east, then 350 m west. To find the displacement, subtract the distance walked west from the distance walked east. 800 m - 350 m = 450 m. This means the person's displacement is 450 m east.", "rejected": "I walked 800 m east and then 350 m west. To find the displacement, I think I just need to add these distances together because that's the total distance I traveled. So, the displacement should be 800 m + 350 m = 1150 m.", "rejected_misconception_id": "MC04"}
{"id": "physics-v1-K6-R1-22e5357f-a0", "prompt": "A marble and a steel shot put are dropped at the same moment from a height of 10 m. Ignore air resistance. Which statement is correct?\nA) A steel shot put hits the ground first.\nB) They hit the ground at the same time.\nC) A steel shot put falls faster, in proportion to how much heavier it is.", "chosen": "In a vacuum, all objects fall at the same rate regardless of their mass. Since air resistance is ignored, the marble and the steel shot put will fall at the same rate and hit the ground at the same time. The correct answer is B.", "rejected": "Since the steel shot put is much heavier than the marble, it should fall faster and hit the ground first. Therefore, the answer is A.", "rejected_misconception_id": "MC01"}
{"id": "physics-v1-K7-R1-13b3e76d-a0", "prompt": "From a height of 5.0 m, one ball is dropped while an identical ball is launched horizontally at 3 m/s at the same instant. Ignore air resistance. Which statement is correct?\nA) The launched ball lands first, because it is moving faster.\nB) The launched ball lands later, because its horizontal speed keeps it in the air.\nC) Both balls land at the same time.", "chosen": "Both balls experience the same gravitational acceleration in the vertical direction, regardless of their horizontal speed. The time it takes for each ball to fall 5.0 m is determined solely by the vertical motion. Since both balls fall the same distance under the same acceleration, they land at the same time. The correct answer is C.", "rejected": "I think the launched ball will land first because it's moving faster horizontally. Since it's moving faster, it should hit the ground sooner than the ball that is just dropped straight down. So, I choose A.", "rejected_misconception_id": "MC13"}
{"id": "physics-v1-N4-R1-5553fe5d-a0", "prompt": "A truck collides head-on with a small car. During the collision, how do the forces they exert on each other compare?\nA) Only a truck exerts a force; a small car just gets pushed.\nB) A truck exerts a larger force on a small car than a small car exerts on it.\nC) The forces are equal in size and opposite in direction.", "chosen": "According to Newton's Third Law, for every action, there is an equal and opposite reaction. This means that the force the truck exerts on the small car is equal in size and opposite in direction to the force the small car exerts on the truck. The correct answer is C.", "rejected": "I think the truck exerts a larger force on the small car because it's bigger and heavier. The small car just gets pushed, so the force it exerts is not as important. Therefore, I choose A.", "rejected_misconception_id": "MC09"}
{"id": "physics-v1-N5-R3-2f67b1dc-a0", "prompt": "A factory has a piece of machinery with a mass of 12 kg placed on the Earth's surface. Calculate the weight of this machinery in newtons, given g = 9.8 m/s².", "chosen": "The weight of an object is given by the mass multiplied by the gravitational acceleration. So, weight = 12 kg × 9.8 m/s². Therefore, weight = 118 N.", "rejected": "To find the weight of the machinery, I simply use the mass which is given as 12 kg. Since weight is the same as mass, the weight of the machinery is 12 N.", "rejected_misconception_id": "MC18"}
{"id": "physics-v1-E1-R3-4bdc0d81-a0", "prompt": "A child pulls a sled 10 m across level snow in a playground using a rope that makes a 30° angle with the ground. The tension in the rope is 50 N. How much work does the rope do on the sled?", "chosen": "Find the component of the force that acts in the direction of motion: 50 N × cos(30°) = 50 N × 0.866 = 43.3 N. Calculate the work done by multiplying the force component by the distance: 43.3 N × 10 m = 433 J.", "rejected": "I think the work is just the force times the distance because the angle doesn't matter. So, 50 N times 10 m equals 500 J.", "rejected_misconception_id": "MC17"}
{"id": "physics-v1-E2-R3-3da3077d-a0", "prompt": "An object with a mass of 1200 kg is moving at a speed of 20 m/s on a construction site. Calculate the kinetic energy of this object.", "chosen": "Kinetic energy formula: KE = ½·m·v². Plugging in the values: KE = ½ × 1200 kg × (20 m/s)². Calculating the speed squared: (20 m/s)² = 400 m²/s². Calculating the kinetic energy: KE = ½ × 1200 × 400 = 240000 J. The kinetic energy of the object is 240000 J.", "rejected": "To find the kinetic energy, I use the formula that I thought was correct, KE = ½·m·v. So, I take the mass, which is 1200 kg, and the speed, which is 20 m/s, and calculate: KE = ½ × 1200 × 20 = 12000 J.", "rejected_misconception_id": "MC14"}
{"id": "physics-v1-E5-R4-213f7ba0-a0", "prompt": "A skier starts from rest at the top of a ski ramp that is 4 m high and inclined at 45°. The coefficient of kinetic friction between the skier's skis and the ramp is 0.3. Assuming the skier's mass remains constant, how fast is the skier moving at the bottom of the ramp? (You may use g = 9.8 m/s².)", "chosen": "The ramp length is calculated as 5.66 m, and the work done by friction per kg is 11.8 J. Initial potential energy is 4 m × 9.8 m/s² = 39.2 J/kg. Work done by friction = 11.8 J/kg, subtract from initial potential energy to get final kinetic energy: 39.2 J/kg - 11.8 J/kg = 27.4 J/kg. Final kinetic energy 27.4 J/kg = 0.5 × v²; solving, v = 7.41 m/s.", "rejected": "I used the principle of conservation of energy, assuming no friction affects the skier's speed. The potential energy at the top, 4 m × 9.8 m/s², equals the kinetic energy at the bottom, 0.5 × v². Solving for v, I get 8.85 m/s.", "rejected_misconception_id": "MC16"}