A body moving with velocity v can be stopped by a force F in direction of it. Same body moving with velocity 5v can be stopped by a force 5F in distance equal to:
Correct answer: B. 5X
- A. X
- B. 5X
- C. 10X
- D. X/2
Explanation
To find the stopping distance, we use the work-energy principle, which states that the work done by the force is equal to the change in kinetic energy. Initially, the work done is F * X = 1/2 * m * v2. For the new scenario, we have 5F * X' = 1/2 * m * (5v)2, which simplifies to 5F * X' = 1/2 * m * 25v2. Dividing both sides by 5, we get F * X' = 1/2 * m * 5v2, leading to X' = 5X. Thus, the stopping distance is five times greater due to the increased kinetic energy from the higher velocity, while the increased force balances this to maintain a proportional relationship.Options A, C, and D are incorrect because they do not appropriately account for the changes in both velocity and force in accordance with the work-energy principle.
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