Question

Engine of a vehicle can give it an acceleration of 1 ms^-2 and its brakes can retard it at 3 ms^-2. The minimum time in which the vehicle can make a journey between stations A and B having a distance of 1200 m is

• A. 55.6 s
• B. 65.6 s
• C. 50.6 s
• D. 56.5 s

Answer 1

Answer: (D)

56.5 s

Answer 2

During acceleration v/t₁ = 1 t₁ = v

During retardation, v/t₂ = 3 or t₂ = v/3

Using s = 1/2 v(t₁ + t₂) [Displacement = area of ∆]

or 1200 = 1/2 v(v + v/3)

or 1200 = 2v³/3

or v² = 3600/2 = 1800

or v = 42.4

∴ t₁ + t₂ = 42.4 + 42. 4/3 = 56.5 s