A particle moves in a straight line with a retardation proportional to its displacement. Its loss of kinetic energy for any displacement is proportional to

Question

A particle moves in a straight line with a retardation proportional to its displacement. Its loss of kinetic energy for any displacement  is proportional to

Canvas Classes · Accepted Answer

🧠 Loss of Kinetic Energy = Work Done Against the Force

The retardation is proportional to displacement, so  and the retarding force is  — exactly like a spring. The kinetic energy the particle loses while moving a distance  equals the work this force takes out of it. So the question is really: what is  when  grows linearly with ?

🗺️ Working It Out

The force opposing the motion has magnitude .

Loss in KE .

So the loss of kinetic energy is proportional to .

⚡ The Smart Move

This is the wo

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