A particle starts with speed u and obeys a = kv. The distance travelled when its speed first becomes 2u is:
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A particle starts with speed u and obeys a = kv. The distance travelled when its speed first becomes 2u is:

G1 Physics · Accepted Answer

Use a = v dv/dx. Then v dv/dx = kv ⇒ dv/dx = k. Integrating from v=u at x=0, v = u + kx. For v=2u, 2u = u+kx ⇒ x = u/k.