Question

two identical car running on highway with 20m/s and 40m/s respectively applied by same retarding force ,the ratio of stoping distance is what​

Answer 1

Given:-

initial velocity of first car = u₁ = 20 m/s

initial velocity of second car = 40 m/s

Retarding force on both cars is same

To find:-

▪ As the retarding force is same on both cars, and the the cars are identical (which means they have the same mass), the retardation (negative acceleration) is also equal on both cars (since a = F/m)

▪Formula ➩ v² = u² + 2as where v is final velocity, u is initial velocity, a is acceleration and s is displacement.

▪ Let acceleration = a = -A, (for both cars) since it causes retardation.

▪ final velocity = v = 0 for both cars since they will finally come to rest.

For first car:-

v₁² = u₁² + 2a₁s₁

→ 0² = 20² + 2(-A)(s₁)

→ 2As₁ = 400

→ s₁ = 200/A

▪For second car:-

v₂² = u₂² + 2a₂s₂

→ 0² = 40² + 2(-A)(s₂)

→ 2As₂ = 1600

→ s₂ = 800/A

▪Ratio of stopping distance of first and second car:-

s₁/s₂ = [(200/A) / (800/A)]

→ s₁/s₂ = 200/800

→ s₁/s₂ = 1/4

→ s₁ : s₂ = 1 : 4 Ans.