A particle starts with speed u and its acceleration is a = -kv, where k>0. The distance travelled by the time its speed becomes u/4 is:
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A particle starts with speed u and its acceleration is a = −kv, where k>0. The distance travelled by the time its speed becomes u/4 is:

G1 Physics · Accepted Answer

Using a = v dv/dx, v dv/dx = −kv. For v>0, dv/dx = −k. Hence v = u − kx. When v=u/4, u/4 = u − kx ⇒ kx = 3u/4 ⇒ x = 3u/(4k).