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? A)5 s B)10 s C)15 s D)20 s E)25 s

Question

Quizplus · Accepted Answer

First, we need to find the distance the truck travels during the time taken by the car to catch up to it.
Let t be the time taken by the car to catch up to the truck.
Distance traveled by the truck = speed × time = 15t
Distance traveled by the car = (1/2)acceleration × time² = (1/2)(3)t² = (3/2)t²
The car catches up to the truck when the distances traveled by both are equal.
Therefore, 15t = (3/2)t²
Simplifying the equation, we get t = 10 seconds.
Therefore, the car takes 10 seconds to catch up to the truck. 
The answer is B, 10 s.

At a Stop Light, a Truck Traveling at 15 M/s