The motion of a body is given by dv/dt = 6.0-3v(t), where v is in m s⁻¹ and t in s. If the body is at rest at t=0, find the wrong option.
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Question

The motion of a body is given by dv/dt = 6.0-3v(t), where v is in m s⁻¹ and t in s. If the body is at rest at t=0, find the wrong option.

G1 Physics · Accepted Answer

dv/dt=6-3v has solution v=2(1-e⁻³ᵗ), so terminal speed is 2 m s⁻¹ and initial acceleration is 6 m s⁻². Half the initial acceleration means a=3, so 6-3v=3 ⇒ v=1 m s⁻¹, not 0.1 m s⁻¹. Hence option C is wrong.