At a stop light, a truck traveling at 15 m/s passes a car as it starts from rest. The truck travels at constant velocity, and the car accelerates at 3 m/s². How much time does the car take to catch up to the truck?
Correct answer: C. 10 s
- A. 5 s
- B. 15 s
- C. 10 s
- D. 20 s
Explanation
Correct. Here's the calculation:Distance traveled by the truck:Distance_truck = velocity_truck * timeDistance_truck = 15t (where t is the time taken)Distance traveled by the car:Distance_car = initial_velocity_car * t + (1/2) * acceleration_car * t²Distance_car = 0 * t + (1/2) * 3 * t²Distance_car = 1.5t²When the car catches up, the distances are equal:Distance_truck = Distance_car15t = 1.5t²Solve for t:1.5t² - 15t = 01.5t(t - 10) = 0t = 0 (initial time) or t = 10 sTherefore the time taken is 10 seconds
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