Solving for time with an non consistant acceleration

[laketri]

Problem
Several students are riding in bumper cars at an amusement park. The mass of car A and its occupants is 250kg. The combined mass of car B and its occupants is 200kg. Car A is 15m away away from car B and moving to the right at 2.0m/s, as shown, when the driver decides to bump into car B, which is at rest.

(A) Car A accelerates at 1.5m/s² to a speed of 5.0m/s and then continues at a constant velocity until it strikes car B. Calculate time for car A to travel the 15m.

Attmept
I assumed that you would use v=d/t until I realized that velocity isn't constant. So I looked to the kinematic equations, and thought i would use d=v_i*t+1/2*a*t² until i noticed that acceleration isn't constant either.

I'm going into AP Physics B after I took Honors Physics last year. I've never had to work with non constant acceleration before and I don't know what to do with it. I've looked online and never found anything relevant to what I need.

I don't want an answer to the question, I just need to know what I use to get to the answer.

 

[CWatters]

You didn't post the diagram.

Can you break it down into two parts. eg The time spent under constant acceleration and the time spent at constant velocity?

 

[laketri]

You didn't post the diagram.

I didn't paste the diagram because it is an actual paper and I don't have a scanner, so there's no way for me to, sorry.

Can you break it down into two parts. eg The time spent under constant acceleration and the time spent at constant velocity?

I can't break down the time because that's what I'm solving for, unless I don't understand you correctly

 

[SteamKing]

You should take CWatters advice. Let's catalog what you know about Car A:

Mass of Car A + occupants = 250 kg
Distance Car A to Car B = 15 m

Initial velocity of Car A = 2.0 m/s
Final velocity of Car A = 5.0 m/s

Car A accelerates from 2.0 m/s to 5.0 m/s with acceleration of 1.5 m/s^2
How long does this take?
How far does Car A travel while accelerating?
Is this distance < 15 m?
If yes, then figure out how long it takes Car A to from this point until it is 15 m from the starting point, assuming Car A is moving at a constant velocity of 5.0 m/s.

 

[laketri]

You should take CWatters advice. Let's catalog what you know about Car A:

Mass of Car A + occupants = 250 kg
Distance Car A to Car B = 15 m

Initial velocity of Car A = 2.0 m/s
Final velocity of Car A = 5.0 m/s

Car A accelerates from 2.0 m/s to 5.0 m/s with acceleration of 1.5 m/s^2
How long does this take?
How far does Car A travel while accelerating?
Is this distance < 15 m?
If yes, then figure out how long it takes Car A to from this point until it is 15 m from the starting point, assuming Car A is moving at a constant velocity of 5.0 m/s.

So, if i did this right, it would take 2 seconds to accelerate to 5.0m/s
so using d=v_i*t+1/2*a*(t²)
I could find that the distance is 7 m
Then using simple algebra, take 7m away from 15m, then deviding by 5 to get the amount of seconds traveled in 5m/s, I could find the time to be 3.6

 

[haruspex]

So, if i did this right, it would take 2 seconds to accelerate to 5.0m/s
so using d=v_i*t+1/2*a*(t²)
I could find that the distance is 7 m
Then using simple algebra, take 7m away from 15m, then deviding by 5 to get the amount of seconds traveled in 5m/s, I could find the time to be 3.6

All correct, except for the 3.6 at the end.

 

[laketri]

All correct, except for the 3.6 at the end.

I was adding the previous 2 seconds to the 1.6 which was received from 15-7/5

 

[haruspex]

I was adding the previous 2 seconds to the 1.6 which was received from 15-7/5

OK, good.