Multiple choice

A car P is moving with a uniform speed of 72 km/h towards another car Q at rest on a straight level road. At a particular instant when the distance between P and Q is 525 m, the car Q started accelerating at 2 m/s2 towards P. Find the distance travelled by Q, when both the cars meet.

  1. 300 m

  2. 225 m

  3. 100 m

  4. 30 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Car P speed = 72 km/h = 20 m/s. Let time to meet be t. Distance P travels = 20t. Distance Q travels = 0.5 * 2 * t^2 = t^2. Total distance = 20t + t^2 = 525. t^2 + 20t - 525 = 0. (t + 35)(t - 15) = 0. t = 15 seconds. Distance Q travels = t^2 = 15^2 = 225 m.

AI explanation

Convert the speed of car P to 20 m/s. Let the two cars meet after t seconds; car P covers 20t meters and car Q covers 0.5 multiplied by 2 multiplied by t squared meters. The equation is 20t + t squared = 525, which factors to (t + 35)(t minus 15) = 0, meaning the time is 15 seconds. The distance travelled by Q is t squared, which is 15 squared or 225 m.

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