Two cars are traveling in the same direction in a straight line along a narrow,

Question

Two cars are traveling in the same direction in a straight line along a narrow, single lane, snowy road. The trailing car is moving at 25.0 m/s, while the lead car is traveling at a slower pace of 15.0m/s. When they come with in 20 m of each other, the trailing car's driver sees the lead car through the falling snow and begins to brake. The driver of the lead car is unaware of the trailing car and continues at the same constant speed. Because of the snow on the ground, the trailing car is only able to decelerate at a rate of 1.00m/s^2. Determine if the two cars are destined to collide with each other.

Explanation / Answer

Consider the motion of trailing car

V = relative velocity of trailling car = 25 - 15 = 10 m/s

d = stopping distance allowed = 20 m

a = acceleration = - 1 m/s2

D = actual stopping distance

Vf = final velocity = 0 m/s

using the equation

V2f = V2 + 2 a D

02 = 102 + 2 (-1)D

D = 50 m

Since D > d

hence the two cars collide

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