The car in front of you is driving 105 km/h on the highway. You pull out to pass the car travelling 114 km/h. Both cars are 2.7m long. You pull out when you are 10m behind the car in front of you and pull back in when you are 10m in front of the other car. How long does it take you to pass the car? How far did you travel?
In relative distance, you travel 2.7x2 meters. Your relative velocity is 9km/hr (change to m/s).
time to pass: relative distance/relative speed
Now, with that time; how far did you travel..
distance=your speed*time.
RELATIVE DISTANCE IS 5.4 METERS
(VELOCITY=SPEED)TO FIND RELATIVE SPEED IN M/S, WE DO THAT A.T.Q.
9*1000/60*60=9000/3600=5/2 =2.5 M/S
TIME TO PASS =5.4/2.5=2.16
DISTANCE=SPEED*TIME
DISTANCE =2.5*2.16 =5.4 METERS
Actually, the two people above are wrong. They did not take into account the 10m travelled behind and in front. The total distance is 25.54 m (10+2.7+10+2.7). The velocity relative to the other car is 9km/h (2.5 m/s). You must use 9 km/h and not 114 km/h because the other car is in motion too. Thus the time is 25.54/2.5, which is 10.16 s. With significant digits, the answer is 10 seconds.
To determine the time it takes you to pass the car and the distance traveled, we can use the concept of relative velocity.
The relative velocity between two objects is the difference between their individual velocities. In this case, the relative velocity is the difference between your car's velocity and the car in front of you.
Relative velocity (v_rel) = Your car's velocity - Car in front's velocity
v_rel = 114 km/h - 105 km/h
First, let's convert the velocities to meters per second (m/s) for consistency:
Your car's velocity = 114 km/h * (1000 m/1 km) * (1 h/3600 s)
Your car's velocity = 31.67 m/s
Car in front's velocity = 105 km/h * (1000 m/1 km) * (1 h/3600 s)
Car in front's velocity = 29.17 m/s
Now, let's calculate the relative velocity:
v_rel = 31.67 m/s - 29.17 m/s
v_rel = 2.5 m/s
To determine the time it takes you to pass the car, we need to calculate the time it takes for the distance between you and the car in front to change by 2.7 m (the combined length of both cars).
Time (t) = Distance (d) / Relative velocity (v_rel)
t = 2.7 m / 2.5 m/s
t = 1.08 seconds
Therefore, it takes you 1.08 seconds to pass the car.
To calculate the distance traveled, we need to determine how far you traveled from the moment you pulled out until you pulled back in.
Distance traveled = Distance in front + Distance between the cars
Distance traveled = 10 m + 2.7 m + 10 m
Distance traveled = 22.7 meters
Therefore, you traveled a distance of 22.7 meters while passing the car.