Cars A and B move in the same direction with speeds Vₐ and Vᵦ, where Vₐ>Vᵦ. A is initially a distance s behind B and then applies brakes with uniform retardation a. Which condition ensures no collision?
Options

Question

Cars A and B move in the same direction with speeds Vₐ and Vᵦ, where Vₐ>Vᵦ. A is initially a distance s behind B and then applies brakes with uniform retardation a. Which condition ensures no collision?

Options

G1 Physics · Accepted Answer

Relative initial speed of A with respect to B is Vₐ-Vᵦ. Since only A retards with magnitude a, the relative stopping distance is (Vₐ-Vᵦ)²/(2a). To avoid collision, the initial separation must be at least this value: s≥(Vₐ-Vᵦ)²/(2a). Hence option C. The printed source key appears inconsistent.

Cars A and B move in the same direction with speeds Vₐ and Vᵦ, where Vₐ&gt;Vᵦ. A is initially a distance s behind B and then applies brakes with uniform retardation a. Which condition ensures no collision?

Cars A and B move in the same direction with speeds Vₐ and Vᵦ, where Vₐ>Vᵦ. A is initially a distance s behind B and then applies brakes with uniform retardation a. Which condition ensures no collision?