The displacement x of a particle varies with time t as x = ae⁻ᵅᵗ + beᵝᵗ, where a, b, α and β are positive constants. The velocity of the particle will:
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Question

The displacement x of a particle varies with time t as x = ae⁻ᵅᵗ + beᵝᵗ, where a, b, α and β are positive constants. The velocity of the particle will:

G1 Physics · Accepted Answer

Step 1: Differentiate: v = dx/dt = −aαe⁻ᵅᵗ + bβeᵝᵗ. Step 2: Differentiate again: dv/dt = aα²e⁻ᵅᵗ + bβ²eᵝᵗ. Step 3: Every term in dv/dt is positive because a, b, α and β are positive. Hence velocity increases continuously with time. Final answer: D.