A blue car moving at constant speed of 10m/s passes a polic car that is at rest. The police car accelerates from rest at 4m/s^2 for 3.0 seconds and then maintains a constant speed. The blue car maintains constant speed for the entire 12 seconds. When does the police car pass the blue car?
Calculations:
Blue Car:
Vi= 10 m/s
Vf = 10 m/s
deltaT = 12 s
deltaD = 120 m
acceleration = 0
Police Car:
Vi = 0m/s
acceleration = 4m/s^2 (for the first 3 seconds)
deltaD (for first three seconds) = 18 m
Vf = 12 m/s
So when the deltaD of the blue car = the deltaD of the police car, the police car is at the same distance as the blue car.
How would I go about doing this?
A blue car moving at constant speed of 10m/s passes a polic car that is at rest. The police car accelerates from rest at 4m/s^2 for 3.0 seconds and then maintains a constant speed. The blue car maintains constant speed for the entire 12 seconds. When does the police car pass the blue car?
The police car accelerates at 4m/s^2 for 3 seconds reaching a final speed of 12m/s^2 and traveling a distance of at^2/2 = 4(3^2)/2 = 18m.
At this 3 second point, the blue car has traveled 3(10) = 30m.
From this point on, the police car will close the existing gap of 12m between the cars at a closing speed of 12 - 10 = 2m/s.
Thus, the police car will overtake, and pass the blue car in 12/2 = 6 seconds or 9 seconds after the blue car started.
ME NO MO
To determine when the police car passes the blue car, we need to calculate the time it takes for the police car to cover the same distance as the blue car.
1. Calculate the distance traveled by the police car during the first 3 seconds, when it is accelerating:
- Using the formula: deltaD = Vi * deltaT + (1/2) * acceleration * (deltaT)^2
- Vi = 0 m/s (initial velocity of the police car)
- deltaT = 3 s (time interval for acceleration)
- acceleration = 4 m/s^2 (acceleration of the police car)
- Substitute these values into the formula to find deltaD (distance traveled during acceleration).
2. Subtract the distance covered during acceleration from the total distance covered by the police car to find the remaining distance at constant speed:
- Let's call this remaining distance deltaD_constant_speed.
- deltaD_constant_speed = deltaD_total - deltaD_acceleration
- deltaD_total = 120 m (total distance covered by the police car)
- deltaD_acceleration = distance covered during acceleration (calculated in step 1)
3. Calculate the time it takes for the police car to cover the remaining distance at a constant speed:
- Calculate the time using the formula: deltaT_constant_speed = deltaD_constant_speed / Vf
- Vf = 12 m/s (final velocity of the police car after acceleration)
- Substitute the values to find deltaT_constant_speed (time taken during constant speed).
4. Add the time taken during acceleration (3 seconds) to the time taken during constant speed to find the total time for the police car to catch up to the blue car:
- Total time = 3 s (time for acceleration) + deltaT_constant_speed (time for constant speed)
By following these steps, you should be able to determine when the police car passes the blue car.