A particle starts with speed u and obeys a = -kv². The distance travelled before its speed becomes u/2 is:
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A particle starts with speed u and obeys a = −kv². The distance travelled before its speed becomes u/2 is:

G1 Physics · Accepted Answer

Use a = v dv/dx: v dv/dx = −kv². For v>0, dv/dx = −kv. Thus dx = −dv/(kv). Integrating from u to u/2, x = (1/k)ln(u/(u/2)) = ln2/k.