Kinematics 1-D Problem. Stuck on specific parts.

[Jabran Shakil]

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 3.1 m/s2 for 3.7 seconds. It then continues at a constant speed for 12.5 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 176 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop.1). How fast is the blue car going 1.1 seconds after it starts? 3.41

2). How fast is the blue car going 11.6 seconds after it starts? 11.47

3). How far does the blue car travel before its brakes are applied to slow down? 164.59

4). What is the acceleration of the blue car once the brakes are applied?

5). What is the total time the blue car is moving?

6). What is the acceleration of the yellow car?

I can't seem to figure out numbers 4-6. I've been stuck on them for a good hour now.

 

[Kilgour22]

Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 3.1 m/s2 for 3.7 seconds. It then continues at a constant speed for 12.5 seconds, before applying the brakes such that the car’s speed decreases uniformly coming to rest 176 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop.1). How fast is the blue car going 1.1 seconds after it starts? 3.41

2). How fast is the blue car going 11.6 seconds after it starts? 11.47

3). How far does the blue car travel before its brakes are applied to slow down? 164.59

4). What is the acceleration of the blue car once the brakes are applied?

5). What is the total time the blue car is moving?

6). What is the acceleration of the yellow car?

I can't seem to figure out numbers 4-6. I've been stuck on them for a good hour now.

For #4, what do we know about the final velocity of the blue car?

For #5, which time interval are we missing in order to find the total time, and what do we need to know in order to find that time interval?

For #6, think about the formula $\Delta{x} = v_{0x}\Delta{t} + \frac{1}{2}a_{x}\Delta{t^2}$. What is/are the constant variable(s) that is/are shared between both the blue and yellow cars that we can use?

 

[thecommexokid]

Re: 4

You know the speed the car was going when it started braking, the speed when it completed braking, and the distance it took to brake. Can you use those facts to determine the acceleration?

Re: 5

You are told the total time for segments 1 and 2, so we only need to figure out how long the braking segment takes. You know the distance, and once you've done no. 4 then you know the acceleration. Can you determine the time from that?

Re: 6

What is the total time the yellow car is moving? (Hint: how does this relate to the total time the blue car is moving?

 

[thecommexokid]

Re: 4

You know the speed the car was going when it started braking, the speed when it completed braking, and the distance it took to brake. Can you use those facts to determine the acceleration?

Re: 5

You are told the total time for segments 1 and 2, so we only need to figure out how long the braking segment takes. You know the distance, and once you've done no. 4 then you know the acceleration. Can you determine the time from that?

Re: 6

What is the total time the yellow car is moving? (Hint: how does this relate to the total time the blue car is moving?

PS: I agree with your stated answers for 1–3, except that they are missing units.

 

[Jabran Shakil]

Okay so Number 4, the Final Velocity is 0 since it's stopped, right?

 

[thecommexokid]

applying the brakes such that the car’s speed decreases uniformly coming to rest

Okay so Number 4, the Final Velocity is 0 since it's stopped, right?

I agree.