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A 5 kg block is moving along the x-axis under the influence of a force given by F = (−20x + 10) N, where x is in meters. At t = 0 seconds, the block is initially at rest at x = 1 meter. What are the block's position and momentum at t = (π/4) seconds?

1. -0.5 m, 5 kg·m/s
2. 0.5 m, 0 kg·m/s
3. 0.5 m, -5 kg·m/s
4. -1 m, 5 kg·m/s

Correct answer: 0.5 m, -5 kg·m/s

Solution

The block's position and momentum at t = (π/4) seconds are 0.5 m and -5 kg·m/s because the force acting on the block is given by F = (−20x + 10) N, which can be used to find the equation of motion, and solving this equation with the given initial conditions yields the position and momentum at the specified time.

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