A sports car is travelling along a highway at a constant velocity of 36 m/s [N] exceeding the speed limit. It passes an unmarked police car parked on the shoulder of the highway. The police car accelerates from rest, 3.0 s after the sports car passed it, at the rate of 6.0 m/s2 [N] until it reaches a velocity of 48 m/s [N]. It maintains this velocity until it catches up to the sports car.
Well, well, well, looks like the police car wants to race! It's like they're saying, "Hey, sports car, buckle up! I'm coming for ya!" I gotta say, though, the police car seems pretty eager to catch up, accelerating from rest at 6.0 m/s². I guess they really want to make up for lost time.
Now, let's calculate how long it takes for the police car to catch up with the sports car. The initial velocity of the sports car and the time it took to accelerate are given, so we can use some good ol' physics to figure it out.
First, we need to find out how far the sports car traveled during those 3.0 seconds. We can use the formula: distance = velocity x time. So, distance = 36 m/s x 3.0 s = 108 m.
Now, the police car starts accelerating from rest until it reaches a velocity of 48 m/s. Hmm, that poor police car had to work pretty hard to catch up! Anyway, to find out how long it took, we can use another formula: velocity = acceleration x time. So, 48 m/s = 6.0 m/s² x time. That gives us time = 8 seconds.
Now comes the fun part! The police car caught up to the sports car after 8 seconds, which means they traveled at the same rate for 8 seconds. Since we know the velocity of the police car is 48 m/s, we can calculate the distance they traveled: distance = velocity x time. So, distance = 48 m/s x 8 s = 384 m.
So, after all those calculations, the police car catches up to the sports car after traveling 384 m, or as they say in the racing world, "game over, sports car!" I hope they both learned their lesson about speeding. Remember, folks, always drive safely and obey the speed limits or you might end up in a high-speed chase with a determined police car! Stay safe out there, folks!
To find the time it takes for the police car to catch up to the sports car, we can use the equations of motion.
First, let's find the time it takes for the police car to reach a velocity of 48 m/s. We know the initial velocity (u) of the police car is 0 m/s, the acceleration (a) is 6.0 m/s^2, and the final velocity (v) is 48 m/s. The equation we can use is:
v = u + at
Rearranging the equation to solve for time (t):
t = (v - u) / a
Substituting the values:
t = (48 m/s - 0 m/s) / 6.0 m/s^2
t = 8 seconds
So, it takes the police car 8 seconds to reach a velocity of 48 m/s.
Now, let's find the time it takes for the sports car to travel during those 8 seconds. The sports car is travelling at a constant velocity of 36 m/s, so the distance it covers can be calculated using the equation:
distance = velocity × time
Substituting the values:
distance = 36 m/s × 8 s
distance = 288 meters
Therefore, during the 8 seconds it takes the police car to accelerate to a velocity of 48 m/s, the sports car has traveled 288 meters.
Since the police car starts 288 meters behind the sports car, it needs to cover this distance in order to catch up to the sports car. The time it takes for the police car to catch up to the sports car is determined by the equation:
distance = velocity × time
Substituting the values:
288 meters = 48 m/s × time
Solving for time:
time = 288 meters / 48 m/s
time = 6 seconds
Thus, it will take the police car 6 seconds to catch up to the sports car.