Velocity,time,acceleration question

[drinkingstraw]

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?

 

[CompuChip]

Note how this problem is similar to this question.
Probably if you solve the other one, you will be able to do this one yourself.

 

[nlightner]

To find the time when the police car passes the blue car, we can set up a distance equation:
Distance of blue car = Distance of police car
Since the blue car maintains constant speed for the entire 12 seconds, its distance can be calculated using the formula:
Distance = Initial Velocity x Time
Therefore, for the blue car, the equation would be:
120m = 10m/s x t
Solving for t, we get t = 12 seconds

For the police car, we need to consider the two parts of its motion - the first 3 seconds when it accelerates and the remaining 9 seconds when it maintains constant speed.
For the first 3 seconds, we can use the formula:
Distance = Initial Velocity x Time + (1/2) x Acceleration x Time^2
Substituting the values, we get:
18m = 0 x 3s + (1/2) x 4m/s^2 x (3s)^2
Simplifying, we get 18m = 18m, which is true. This confirms that the distance covered by the police car in the first 3 seconds is 18m.

For the remaining 9 seconds, we can use the formula:
Distance = Initial Velocity x Time
Substituting the values, we get:
Distance = 12m/s x 9s
Distance = 108m

Now, to find the time when the police car passes the blue car, we can set up another distance equation:
Distance of blue car = Distance of police car
Substituting the values, we get:
120m = 18m + 108m
Simplifying, we get 120m = 126m
This means that after 9 seconds, the police car has already covered 126m, which is more than the distance of the blue car. Therefore, the police car passes the blue car after 9 seconds.

In summary, the police car passes the blue car after 9 seconds.