A particle starts with velocity u0 and obeys a=−kv. Which statements are correct?

Question

A particle starts with velocity u>0 and obeys a=−kv. Which statements are correct?

G1 Physics · Accepted Answer

From dv/dt=−kv, v=ue⁻ᵏᵗ. Also, using a=v dv/dx, v dv/dx=−kv ⇒ dv/dx=−k ⇒ v=u−kx. As t→∞, v→0 and x→u/k. The velocity approaches zero asymptotically; exact rest is not reached at a finite time. Therefore A, B and C are correct.