I solved few questions on kinematics -- Is my working correct?

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  • #1
Aichuk
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So the first question is:

A student standing on the platform of a railway station notices the first two carriages of an arriving train pass her in 2.0 s and the next two in 2.4 s. The train is decelerating uniformly. Each carriage is 20 m long. When the train stops, the student is opposite the last carriage. How many carriages are there?

My working went:

Avg. Velocity for first two carriages (Va) = 40 m/ 2.0 s = 20 m/s
Avg. Velocity for first two carriages (Vb) = 40 m/ 2.4 s = 16.7 m/s (correct to 3 significant figures).

Time at Va = 2.0 s / 2 = 1s

Time at Vb = 2 s + (2.4 s / 2) = 3.2 s

Acc. = (16.7 - 20 ) m/s / 2.2s = -1.5 ms^-2

At time = 1 s

Va = u + at
20 m/s = u - 1.5 m/s
Therefore, u = 21.5 m/s

Therefore, total time taken is

0 m/s = 21.5 m/s + (-1.5)(t)
t = -21.5/-1.5 = 14.3 s

So total distance is

s = ut + 1/2 at^2
= (21.5 m/s) (14.3s) + (-1.5 ms^-2) (1/2) (14.3^2)
=154 (approx.)

So by dividing the distance by the number of carriages,
154/20 = 7.7
approximated to 8 carriages

It matches with the answer in my book but is the way I solved the answer correct?

Also the next question is more about a concept. So check whether my answer is correct on this too..

In a manual, it's suggested that when driving at 13 m/s, a driver should always keep a minimum of two cars-lengths between the driver's car and the one in front.

Suggest a scientific justification, making reasonable assumptions for magnitudes of any quantities.


So my answer for (a) is that since that a car has a large mass and is moving relatively fast, so it has a high inertia. Thus it takes a large force for it to decelerate quickly so the minimum of two cars-length will allow it to steadily decelerate and come to rest. Any smaller space may cause the car to have to decelerate so quickly that the driver may be injured. Or it may not allow the car to decelerate and come to rest, causing it to hit the car in front.

I'm really doubtful of my answer to the second question especially my phrasing of the answer. Sorry for the long post, I just need some help. Thanks :)
 
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  • #2
Aichuk said:
So the first question is:

A student standing on the platform of a railway station notices the first two carriages of an arriving train pass her in 2.0 s and the next two in 2.4 s. The train is decelerating uniformly. Each carriage is 20 m long. When the train stops, the student is opposite the last carriage. How many carriages are there?

My working went:

Avg. Velocity for first two carriages (Va) = 40 m/ 2.0 s = 20 m/s
Avg. Velocity for first two carriages (Vb) = 40 m/ 2.4 s = 16.7 m/s (correct to 3 significant figures).

Time at Va = 2.0 s / 2 = 1s

Time at Vb = 2 s + (2.4 s / 2) = 3.2 s

Acc. = (16.7 - 20 ) m/s / 2.2s = -1.5 ms^-2

At time = 1 s

Va = u + at
20 m/s = u - 1.5 m/s
Therefore, u = 21.5 m/s

Therefore, total time taken is

0 m/s = 21.5 m/s + (-1.5)(t)
t = -21.5/-1.5 = 14.3 s

So total distance is

s = ut + 1/2 at^2
= (21.5 m/s) (14.3s) + (-1.5 ms^-2) (1/2) (14.3^2)
=154 (approx.)

So by dividing the distance by the number of carriages,
154/20 = 7.7
approximated to 8 carriages

It matches with the answer in my book but is the way I solved the answer correct?

I like the logical way you solved it. I'm not sure why you doubt yourself.

You might have polished it off a little quicker. Once you have ##u## and ##t##, then (for constant deceleration from ##u## to ##0##) you have:

##s = ut/2##
 
  • #3
hi can you please tell me what book you're referring to?
thanks :)
 
  • #4
Meian man said:
hi can you please tell me what book you're referring to?
thanks :)
:welcome:

This thread is over five years old!
 
  • #5
This question is from the book Cambridge International AS & A Level Physics Student's Book 3rd edition END OF TOPIC QUESTIONS 1 in chapter 2
 

Related to I solved few questions on kinematics -- Is my working correct?

1. How can I check if my kinematics solution is correct?

There are a few things you can do to check if your kinematics solution is correct. First, make sure you have correctly applied the equations and concepts to the given problem. You can also check your solution by using different methods or approaches to see if you get the same answer. Additionally, you can compare your solution to a known correct solution or ask for feedback from a peer or instructor.

2. What are some common mistakes to watch out for when solving kinematics problems?

Some common mistakes to watch out for when solving kinematics problems include misinterpreting the given information, using the wrong equations, and making calculation errors. It's important to double-check your work and carefully analyze the problem before jumping into solving it.

3. What should I do if I get stuck on a kinematics problem?

If you get stuck on a kinematics problem, take a step back and review the given information and what the problem is asking for. You can also try breaking the problem down into smaller parts or using diagrams to visualize the situation. If you're still stuck, don't be afraid to ask for help from a classmate or instructor.

4. Is it necessary to show all of my work when solving kinematics problems?

Yes, it's important to show your work when solving kinematics problems. This not only helps you keep track of your thought process but also allows others to follow your reasoning and provide feedback if needed. Additionally, showing your work can earn you partial credit even if your final answer is incorrect.

5. What other resources can I use to improve my understanding of kinematics?

There are many resources you can use to improve your understanding of kinematics. These include textbooks, online tutorials, practice problems, and working with a study group. You can also seek help from your instructor or attend review sessions for additional support.

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