Multiple choice

Two cars left place $A$ simultaneously and reached the place $B$ in $2$ hrs. The.first car travelled half the distance with a speed of $30$ km/hr and the other half at a speed of $45$ km/hr. The second car at the same time covered the entire distance with a constant acceleration starting from rest. Find the acceleration of the second car.

  1. $36 km/hr^2$
  2. $18 km/hr^2$
  3. $72 km/hr^2$
  4. $144 km/hr^2$
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A Correct answer
Explanation

The first car takes D/2 ÷ 30 + D/2 ÷ 45 = D/36 hours, so D = 72 km. For the second car, 72 = 1/2 × a × 2^2, giving a = 36 km/hr^2.

AI explanation

First, find the total distance by equating the total time of the first car to 2 hours, giving 2 = (d/2)/30 + (d/2)/45. Solving this equation yields d = 72 km. The second car starts from rest and covers this 72 km in 2 hours with constant acceleration. Using the equation of motion s = ut + 0.5*a*t^2, we get 72 = 0 + 0.5*a*(2^2), which simplifies to 72 = 2a. The acceleration of the second car is 36 km/hr^2.

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