4 ms·
The content of this blog is amazing, thanks for the submission. Regarding E=1/2mv*v, where does the 1/2 come from?
by Jyaif 2y ago
The content of this blog is amazing, thanks for the submission.
Regarding E=1/2mv*v, where does the 1/2 come from?
- mikhailfranco 2y agoIt comes from the fact that force is proportional to acceleration (F=ma). Then the factor of 1/2 comes from the formula for the area of a triangle, or equivalently, integrating a constant twice wrt time, gives term in t, then a term in t²/2. Consider constant force acting on a mass initially at rest, for time t producing final velocity v and distance travelled x. F = ma [Newton's 2nd Law] v = at = (F/m)t, so mv = Ft [momentum transfer is force times time] x = (1/2)vt [area under v-t curve: triangle formula] E = Fx = F(1/2)vt = (1/2)v(Ft) = (1/2)mv²
- jessekv 2y agosee also: https://tauday.com/tau-manifesto#table-quadratic_forms https://tauday.com/tau-manifesto#table-quadratic_forms