Multiple choice

A car A travelling on a straight level road with a uniform speed of $60 km/h$ . it is followed by another car B which is moving with a speed of $70 km/h$, when the distance between them is $2.5 km$, the car B is given a deceleration of $ 20 km /h^2 $ . after how much time will B catch up with A .

  1. $1 hr$
  2. $1/2 hr$
  3. $1/4 hr$
  4. $1/8 hr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = 70 - 60 = 10 km/h. Relative deceleration = 20 km/h^2. Distance = 2.5 km. Using s = ut + 1/2at^2: 2.5 = 10t - 1/2(20)t^2. 2.5 = 10t - 10t^2. 10t^2 - 10t + 2.5 = 0. Divide by 2.5: 4t^2 - 4t + 1 = 0. (2t - 1)^2 = 0. t = 0.5 hours.

AI explanation

Using the relative speed concept, the initial relative speed of B with respect to A is 70 - 60 = 10 km/h. The relative deceleration is 20 km/h^2, meaning the relative speed decreases by 20 km/h every hour. The time taken for the relative speed to become zero is calculated as 10 / 20 = 0.5 hr. At this point, the relative distance covered is 10*0.5 - 0.5*20*0.5^2 = 2.5 km, which exactly matches the initial gap. B catches up with A in 1/2 hr.

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