For a particle, acceleration is defined as a⃗ = -(5x/|x|) î for x ≠ 0 and a⃗ = 0 for x = 0. If the particle is initially at rest at (a, 0), what is the period of motion?
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Question

For a particle, acceleration is defined as a⃗ = −(5x/|x|) î for x ≠ 0 and a⃗ = 0 for x = 0. If the particle is initially at rest at (a, 0), what is the period of motion?

G1 Physics · Accepted Answer

The acceleration has constant magnitude 5 toward x=0. From rest at x=a, the time to reach the origin is found from a=(1/2)(5)t², giving t=√(2a/5). This is one quarter of the complete oscillation, hence T=4√(2a/5) s. Correct answer: A.