A particle starts from rest at x=0 and has acceleration a=a₀cosωt. At t=π/ω, its velocity and displacement are respectively:
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A particle starts from rest at x=0 and has acceleration a=a₀cosωt. At t=π/ω, its velocity and displacement are respectively:

G1 Physics · Accepted Answer

Integrating acceleration, v = ∫₀→t a₀cosωτ dτ = (a₀/ω)sinωt. At t=π/ω, v=0. Now x = ∫₀→t v dτ = (a₀/ω²)(1−cosωt). At t=π/ω, x = (a₀/ω²)(1−cosπ) = 2a₀/ω².