A particle with velocity v=v₀ at t=0 is decelerated at a rate |a|=α√v, where α is positive. Which statements are correct?
Select all that apply

Question

A particle with velocity v=v₀ at t=0 is decelerated at a rate |a|=α√v, where α is positive. Which statements are correct?

G1 Physics · Accepted Answer

dv/dt=-α√v. Integrating: 2√v=2√v₀-αt, so stopping time t=2√v₀/α; A is true. For stopping distance, use v dv/dx=-α√v ⇒ dx=-√v dv/α. Hence x=∫₀→v₀√v dv/α=2v₀³ᐟ²/(3α), so D is true. Correct: A,D.