Kinematics 1-D Problem. Stuck on specific parts.

In summary: So, using the formula ##v_{f} = v_{0} + at##, we can solve for acceleration. We know the final velocity (0 m/s), the initial velocity (11.47 m/s from question 2), and the time (12.5 seconds). This gives us an acceleration of -0.918 m/s2 for the blue car. For #5, the time interval we are missing is the time it takes for the blue car to brake. To find that, we can use the formula ##\Delta{x} = v_{0}t + \frac{1}{2}at^2## and solve for t. We know the initial velocity (11.47 m/s), the acceleration
  • #1
Jabran Shakil
2
0
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.
 
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  • #2
Jabran Shakil said:
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?
 
Last edited:
  • #3
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?
 
  • #4
thecommexokid said:
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.
 
  • #5
Okay so Number 4, the Final Velocity is 0 since it's stopped, right?
 
  • #6
Jabran Shakil said:
applying the brakes such that the car’s speed decreases uniformly coming to rest

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

I agree.
 

1. What is kinematics in 1-D?

Kinematics in 1-D is the study of motion in one dimension, where the object's position, velocity, and acceleration are only influenced by one direction. This means that the object is moving either horizontally or vertically, but not both.

2. How do I identify the type of problem in kinematics 1-D?

To identify the type of problem in kinematics 1-D, you need to look at the given information in the problem. If the object's initial and final positions are given, it is a displacement problem. If the initial and final velocities are given, it is a velocity problem. If the acceleration is given, it is an acceleration problem. If two out of the three variables are given, it is a kinematics equation problem.

3. What are the basic equations used in kinematics 1-D?

The basic equations used in kinematics 1-D are the equations of motion:
- Displacement (Δx = xf - xi)
- Velocity (v = (xf - xi) / t)
- Acceleration (a = (vf - vi) / t)
- Time (t = (xf - xi) / v)
Where xi is the initial position, xf is the final position, vi is the initial velocity, vf is the final velocity, and t is the time.

4. How do I solve a kinematics 1-D problem?

To solve a kinematics 1-D problem, follow these steps:
1. Identify the type of problem (displacement, velocity, acceleration, or kinematics equation)
2. List down the given information and what is being asked in the problem
3. Choose the appropriate equation to solve for the unknown variable
4. Substitute the given values into the equation
5. Solve for the unknown variable
6. Check your answer to make sure it is reasonable and in the correct units.

5. What are some common mistakes made in solving kinematics 1-D problems?

Some common mistakes made in solving kinematics 1-D problems are:
- Not correctly identifying the type of problem
- Using the wrong equation
- Not converting units to match in the equation
- Not considering the direction of motion
- Forgetting to include the correct sign for the direction in the answer.
To avoid these mistakes, it is important to carefully read and understand the problem, double check the units, and always draw a diagram to visualize the problem.

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