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A car traveling 30 m/s [E] attempts to pass a truck that is 25 m in front of it, traveling 35 m/s [E], by accelerating at 3.5 m/s² [E]. However, the truck also accelerates at 1.5 m/s² [E]. How long and how far does it take for the car to pass the truck?

a. 12.8 s, 192 m
b. 16.4 s, 249 m
c. 19.6 s, 310 m
d. 23.3 s, 394 m

User IlSavo
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1 Answer

6 votes

Final answer:

The car takes 8.57 seconds to catch up to the truck and travels a distance of 192.18 meters during that time.

Step-by-step explanation:

To calculate how long and how far it takes for the car to pass the truck, we need to determine the time it takes for the car to catch up to the truck and the distance traveled during that time.

First, let's calculate the time it takes for the car to catch up to the truck. We can use the equation:
t = (vf - vi) / a
where t is the time, vf is the final velocity, vi is the initial velocity, and a is the acceleration. Since the car is traveling at 30 m/s [E] and accelerating at 3.5 m/s² [E], and the truck is traveling at 35 m/s [E] and accelerating at 1.5 m/s² [E], we can calculate the time it takes for the car to catch up to the truck as follows:
Car: t = (0 - 30) / (-3.5) = 8.57 s

Next, let's calculate the distance traveled during that time. We can use the equation:
d = vit + 0.5at²
where d is the distance, vi is the initial velocity, t is the time, and a is the acceleration. Since the car is traveling at 30 m/s [E] and accelerating at 3.5 m/s² [E], we can calculate the distance as follows:
d = 30(8.57) + 0.5(-3.5)(8.57)² = 192.18 m

Therefore, the correct answer is (a) 12.8 s, 192 m.

User Shima
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