A particle of mass m starts from rest at the origin and moves along the x-axis. Its kinetic energy K changes with time as dK/dt=γt, where γ>0 is constant. Which statements are true?
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Question

A particle of mass m starts from rest at the origin and moves along the x-axis. Its kinetic energy K changes with time as dK/dt=γt, where γ>0 is constant. Which statements are true?

G1 Physics · Accepted Answer

Integrate: K=γt²/2=(1/2)mv², so v=t√(γ/m), proportional to t. Hence acceleration and force are constant. A constant one-dimensional force is conservative. Position grows as t², not linearly.

A particle of mass m starts from rest at the origin and moves along the x-axis. Its kinetic energy K changes with time as dK/dt=γt, where γ&gt;0 is constant. Which statements are true?

A particle of mass m starts from rest at the origin and moves along the x-axis. Its kinetic energy K changes with time as dK/dt=γt, where γ>0 is constant. Which statements are true?