This question tests AP Physics C: Mechanics skills, specifically understanding and calculating translational kinetic energy from power and time relationships. Power is the rate of energy transfer, so the total energy delivered equals power multiplied by time: E = P×t. In this scenario, the engine delivers 80 kW (80,000 W) for 5.0 seconds, and neglecting losses means all this energy converts to kinetic energy: KE = (80,000 W)(5.0 s) = 400,000 J = 4.0×10⁵ J. Choice A is correct because it properly calculates the total energy delivered as kinetic energy gain. Choice B might incorrectly divide by time again, while choices C and D show calculation errors. To help students: Emphasize the relationship between power, energy, and time (P = E/t). Practice problems involving energy conversions and power calculations to reinforce unit consistency and the meaning of 'neglecting losses'.

This question tests AP Physics C: Mechanics skills, specifically understanding and calculating translational kinetic energy using the work-energy theorem. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = KE_f - KE_i. In this scenario, the skateboarder starts from rest (KE_i = 0) and gravity does 980 J of net work, so the final kinetic energy equals the work done: KE_f = 980 J. Choice A is correct because it directly applies the work-energy theorem, recognizing that all the work done converts to kinetic energy. Choice C might incorrectly assume the work is split between kinetic and potential energy, while choice B might confuse mass with energy. To help students: Emphasize that net work equals change in kinetic energy regardless of the object's mass. Practice identifying when to use work-energy theorem versus conservation of energy approaches.

This question tests AP Physics C: Mechanics skills, specifically understanding and calculating translational kinetic energy. Kinetic energy (KE) is the energy an object possesses due to its motion, calculated using KE = 1/2 mv², where m is mass and v is velocity. In this scenario, a 0.16 kg billiard ball moves at 4.0 m/s just after a collision, requiring calculation of its kinetic energy immediately after impact. Choice B is correct because it correctly applies the kinetic energy formula: KE = 1/2 × 0.16 kg × (4.0 m/s)² = 1/2 × 0.16 × 16 = 1.28 J. Choice A is incorrect because it doubles the correct answer, indicating the student likely forgot the 1/2 factor in the formula. To help students: Use collision problems to reinforce energy calculations before and after impacts. Practice with small masses and velocities to build confidence with decimal calculations and proper unit tracking.

This question tests AP Physics C: Mechanics skills, specifically calculating changes in translational kinetic energy. The change in kinetic energy is calculated as ΔKE = KEf - KEi = 1/2 m(vf² - vi²), where m is mass and v represents velocities. In this scenario, a 60 kg skateboarder increases speed from 5.0 m/s to 11 m/s, requiring calculation of the kinetic energy change. Choice A is correct because ΔKE = 1/2 × 60 kg × [(11 m/s)² - (5.0 m/s)²] = 1/2 × 60 × (121 - 25) = 1/2 × 60 × 96 = 2,880 J = 2.88×10³ J. Choice C is incorrect as it likely calculated the final kinetic energy only, forgetting to subtract the initial kinetic energy. To help students: Emphasize the importance of calculating the difference between final and initial states. Practice problems with both increases and decreases in speed to reinforce proper subtraction order.

This question tests AP Physics C: Mechanics skills, specifically understanding and calculating translational kinetic energy. Kinetic energy (KE) is the energy an object possesses due to its motion, calculated using KE = 1/2 mv², where m is mass and v is velocity. In this scenario, the car has a mass of 1200 kg and reaches a velocity of 25 m/s at the bottom of the hill, requiring application of the formula to find its kinetic energy. Choice A is correct because it correctly applies the kinetic energy formula: KE = 1/2 × 1200 kg × (25 m/s)² = 1/2 × 1200 × 625 = 375,000 J = 3.75×10⁵ J. Choice B is incorrect because it doubles the correct answer, likely from forgetting the 1/2 factor in the formula. To help students: Emphasize memorizing the complete formula including the 1/2 factor, and practice dimensional analysis to verify units. Create visual aids showing the relationship between mass, velocity squared, and kinetic energy to reinforce the formula's structure.

This question tests AP Physics C: Mechanics skills, specifically rearranging the kinetic energy formula to solve for mass. Kinetic energy is given by KE = 1/2 mv², which can be rearranged to m = 2KE/v² when solving for mass. In this scenario, a drag car has kinetic energy 2.0×10⁵ J at speed 20 m/s, requiring calculation of the car's mass. Choice B is correct because rearranging the formula gives: m = 2 × (2.0×10⁵ J) / (20 m/s)² = 4.0×10⁵ / 400 = 1000 kg. Choice A incorrectly uses half this value, possibly from forgetting to multiply by 2 when rearranging the formula. To help students: Practice algebraic manipulation of the kinetic energy formula to solve for different variables. Emphasize checking units and using dimensional analysis to verify calculations are set up correctly.

This question tests AP Physics C: Mechanics skills, specifically calculating changes in translational kinetic energy. The change in kinetic energy is calculated as ΔKE = KEf - KEi = 1/2 m(vf² - vi²), where m is mass and v represents velocities. In this scenario, a 0.20 kg billiard ball slows from 6.0 m/s to 2.0 m/s, requiring calculation of the kinetic energy change. Choice A is correct because ΔKE = 1/2 × 0.20 kg × [(2.0 m/s)² - (6.0 m/s)²] = 1/2 × 0.20 × (4 - 36) = 1/2 × 0.20 × (-32) = -3.2 J. The negative sign indicates energy loss, which is expected when an object slows down. Choice B incorrectly shows a positive change, suggesting the student reversed the subtraction order. To help students: Emphasize that negative ΔKE means energy loss (slowing down) while positive means energy gain (speeding up). Practice with various scenarios to reinforce sign conventions in energy calculations.

This question tests AP Physics C: Mechanics skills, specifically understanding the relationship between power, work, and kinetic energy. Kinetic energy (KE) is the energy an object possesses due to its motion, and power is the rate of energy transfer, where Work = Power × time. In this scenario, a 1000 kg drag car starts from rest and receives constant power of 5.0×10⁴ W for 6.0 s, requiring calculation of the resulting kinetic energy. Choice A is correct because the work done equals the change in kinetic energy: W = P × t = 5.0×10⁴ W × 6.0 s = 3.0×10⁵ J, and since the car starts from rest, this equals the final kinetic energy. Choice B incorrectly uses half the time period, while Choice C doubles the correct answer. To help students: Emphasize the work-energy theorem and how power relates to energy transfer over time. Practice problems involving both constant force and constant power scenarios to distinguish between different energy transfer mechanisms.

This question tests AP Physics C: Mechanics skills, specifically understanding and calculating translational kinetic energy. Kinetic energy (KE) is the energy an object possesses due to its motion, calculated using KE = 1/2 mv², where m is mass and v is velocity. In this scenario, a 70 kg skateboarder starts from rest and reaches 12 m/s at the bottom of a ramp, requiring calculation of the final kinetic energy. Choice A is correct because it correctly applies the kinetic energy formula: KE = 1/2 × 70 kg × (12 m/s)² = 1/2 × 70 × 144 = 5,040 J = 5.04×10³ J. Choice B is incorrect because it doubles the correct answer, suggesting the student forgot the 1/2 factor in the formula. To help students: Use energy conservation problems to show how potential energy converts to kinetic energy. Practice problems that involve both initial and final states to reinforce when kinetic energy is zero (at rest) versus non-zero.

This question tests AP Physics C: Mechanics skills, specifically understanding the work-energy theorem and calculating translational kinetic energy. The work-energy theorem states that the work done on an object equals its change in kinetic energy, and KE = 1/2 mv². In this scenario, a 1500 kg car descends from rest to reach 30 m/s, requiring calculation of the work done by gravity. Choice B is correct because the work done equals the change in kinetic energy: W = ΔKE = KEf - KEi = 1/2 × 1500 kg × (30 m/s)² - 0 = 1/2 × 1500 × 900 = 675,000 J = 6.75×10⁵ J. Choice A incorrectly uses half the correct value, possibly from an arithmetic error. To help students: Reinforce that work done by gravity equals the change in kinetic energy for frictionless motion. Practice energy conservation problems to show the equivalence of gravitational potential energy loss and kinetic energy gain.