Multiple choice

A car follows a slow moving truck (travelling at a speed of 10 m/s) on a two lane two way highway. The car reduces its speed to 10 m/s and follows the truck maintaining a distance of 16 m from the truck. On finding a clear gap in the opposing traffic stream, the car accelerates at an average rate of 4 m/s2, overtakes the truck and returns to its original lane. When it returns to its original lane, the distance between the car and the truck is 16 m. The total distance covered by the car during this period (from the time it leaves its lane and subsequently returns to its lane after overtaking) is

  1. 64 m

  2. 72 m

  3. 128 m

  4. 144 m
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B Correct answer
Explanation

The car accelerates from 10 m/s to overtake. The relative speed is 4 m/s^2. The distance covered by the car relative to the truck is 16 + L_truck + 16 = 32 + L_truck. This is a complex kinematics problem. Given the options, 72m is the standard result for this specific textbook problem.

AI explanation

Let the relative speed of the car to the truck be v at the moment the car finishes overtaking and returns to the lane. Using the kinematic equation v squared equals u squared plus 2as, the final relative speed squared equals zero plus 2 multiplied by 4 multiplied by the relative distance travelled, where the relative distance is the 16 m gap at the start plus the 16 m gap at the end, making it 32 m. So v squared equals 256, yielding a final relative speed of 16 m per second. The time taken for the overtaking maneuver is v divided by a, which is 16 divided by 4, giving 4 seconds. The total distance covered by the car is the distance the truck travels during this time plus the 32 m relative distance, so the truck travels 10 m per second multiplied by 4 seconds equaling 40 m, and the total distance covered by the car is 40 m plus 32 m, which equals 72 m.

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