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A 1,500-kg car and a 3,000-kg SUV truck have the same linear momentum. Which of them has more kinetic energy? O a. Both have the same kinetic energy O b. The SUV truck More information is needed to determine which has more kinetic energy. The car O C. Od.

A 1,500-kg car and a 3,000-kg SUV truck have the same linear momentum. Which of them has more kinetic energy? O a. Both have the same kinetic energy O b. The SUV truck More information is needed to determine which has more kinetic energy. The car O C. Od.

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### Physics Problem: Comparing Kinetic Energy A 1,500-kg car and a 3,000-kg SUV truck have the same linear momentum. Which of them has more kinetic energy? #### Options: - **a.** Both have the same kinetic energy - **b.** The SUV truck - **c.** More information is needed to determine which has more kinetic energy - **d.** The car ### Analysis: In this problem, it is stated that both vehicles have the same linear momentum. Momentum (\(p\)) is given by the formula: \[ p = mv \] where \(m\) is mass and \(v\) is velocity. When two objects have the same momentum but different masses, their velocities must adjust accordingly to maintain equality in their products of mass and velocity (\(mv\)). Kinetic energy (\(KE\)) is given by the formula: \[ KE = \frac{1}{2}mv^2 \] To determine which vehicle has more kinetic energy, consider: - The car has half the mass of the SUV truck, so it must have a higher velocity to achieve the same momentum. - Since kinetic energy depends on the square of the velocity, the car, with a higher velocity, will have more kinetic energy than the SUV truck. Thus, the correct answer is likely **d. The car**.
Transcribed Image Text:### Physics Problem: Comparing Kinetic Energy A 1,500-kg car and a 3,000-kg SUV truck have the same linear momentum. Which of them has more kinetic energy? #### Options: - **a.** Both have the same kinetic energy - **b.** The SUV truck - **c.** More information is needed to determine which has more kinetic energy - **d.** The car ### Analysis: In this problem, it is stated that both vehicles have the same linear momentum. Momentum (\(p\)) is given by the formula: \[ p = mv \] where \(m\) is mass and \(v\) is velocity. When two objects have the same momentum but different masses, their velocities must adjust accordingly to maintain equality in their products of mass and velocity (\(mv\)). Kinetic energy (\(KE\)) is given by the formula: \[ KE = \frac{1}{2}mv^2 \] To determine which vehicle has more kinetic energy, consider: - The car has half the mass of the SUV truck, so it must have a higher velocity to achieve the same momentum. - Since kinetic energy depends on the square of the velocity, the car, with a higher velocity, will have more kinetic energy than the SUV truck. Thus, the correct answer is likely **d. The car**.
Expert Solution
Part 1)

Suppose masses and velocites of car and truck are m1 & m2 and v1 & v2.given that linear momentum of both system are same so m1v1=m2v2v2=m1v1m2...............(1)Kinetic energy of car are K1=12m1v12Kinetic energy of truck are K2=12m2v22From equation (1)K2=12m2m1v1m22K2=12m2m12v12m22K2=12m12v12m2K2=m1m2×12m1v12K2=m1m2×K1K2=15003000×K1K2=12K1....................(2)

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