Derive E_K=½mv² from F=ma, W=Fs and a constant-acceleration equation, first for a body initially at rest and then give the net-work expression for nonzero initial speed u. State the assumptions of your derivation.

Question

Accepted Answer

For u=0, v²=2as, so W=mas=½mv². For u≠0, W_net=½m(v²−u²). Constant mass, constant resultant force/acceleration and straight-line motion are used. Use F as the resultant force and identify W as net work. From v²=u²+2as obtain as=(v²−u²)/2. Substitute into W=mas. Set u=0 to identify kinetic energy relative to rest. Give general energy difference and assumptions.

Reconstruct the kinetic-energy formula

Derive E_K=½mv² from F=ma, W=Fs and a constant-acceleration equation, first for a body initially at rest and then give the net-work expression for nonzero initial speed u. State the assumptions of your derivation.

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Your self-assessment

Derive EK=½mv² from F=ma, W=Fs and a constant-acceleration equation, first for a body initially at rest and then give the net-work expression for nonzero initial speed u. State the assumptions of your derivation.

What a complete response should do

Your self-assessment

Derive E_K=½mv² from F=ma, W=Fs and a constant-acceleration equation, first for a body initially at rest and then give the net-work expression for nonzero initial speed u. State the assumptions of your derivation.