CSSA Trial paper- 2 unit (1 Viewer)

[untitled....]

Alrighty, as homework my teacher gave our 3 unit class an exam paper that we have to complete. But it is very hard, especially question 8 onwards.
Does anyone know where I can get some answers?
Ohh and most people, including many tutors found this question impossible...

A train is travelling at a constant velocity of 80km/h as it passes through a railway station at a town. At the same time a second train commences its journey from rest at the railway station, it accelerates uniformly for 15 minutes until it reaches 100 km/h and maintaines the velocity for another 5 mins.

At this time each train slows down at a constant rate, arriving at the next station at the same time.

Calculate the time taken for the trains to travel between the 2 stations AND how far apart are the stations?


(3, 2 marks)

 

[lyounamu]

Alrighty, as homework my teacher gave our 3 unit class an exam paper that we have to complete. But it is very hard, especially question 8 onwards.
Does anyone know where I can get some answers?
Ohh and most people, including many tutors found this question impossible...

A train is travelling at a constant velocity of 80km/h as it passes through a railway station at a town. At the same time a second train commences its journey from rest at the railway station, it accelerates uniformly for 15 minutes until it reaches 100 km/h and maintaines the velocity for another 5 mins.

At this time each train slows down at a constant rate, arriving at the next station at the same time.

Calculate the time taken for the trains to travel between the 2 stations AND how far apart are the stations?


(3, 2 marks)

Draw a diagram for this.

Distance-time graph is the most effective. If you draw one, you will see what I mean better

For 1st: T1 = 80x20 + (t-20) x 80/2 = 800 + 40t

For 2nd T2 = 5 x 100 + (t-20) x 100/2 + 15 x 100/2 = 250+ 50t

so since T1 = T2

800 + 40t = 250 + 50t
t = 55 minutes

distance: 80 x 1/3 hour + 7/12 x 80/2 = 50 km

(for distance, i changed it to an hourly form because the speed is based on hour)

 

[Drongoski]

Alrighty, as homework my teacher gave our 3 unit class an exam paper that we have to complete. But it is very hard, especially question 8 onwards.
Does anyone know where I can get some answers?
Ohh and most people, including many tutors found this question impossible...

A train is travelling at a constant velocity of 80km/h as it passes through a railway station at a town. At the same time a second train commences its journey from rest at the railway station, it accelerates uniformly for 15 minutes until it reaches 100 km/h and maintaines the velocity for another 5 mins.

At this time each train slows down at a constant rate, arriving at the next station at the same time.

Calculate the time taken for the trains to travel between the 2 stations AND how far apart are the stations?


(3, 2 marks)

Are the answers: 55 mins & 50 km ??

 

[untitled....]

Apparently so!
Thank you both for your help!

 

[Drongoski]

Are the answers: 55 mins & 50 km ??

Say train-A & train-B took T hrs to come to a stop @ the 2nd station. Train-A's acceleration is (0 - 80)/T kph/h; say this last stretch is S-1; then using the well-known (to those who have done elementary kinematics) formula : v^2 = u^2 + 2as (u = initial velocity, v the final velocity, a the acceleration and s the distance covered) we have: 0^2 = 8O^2 + 2 x(-80/T) x S-1 so that S-1 = 40T; similarly we get S-2 = 50T. Now total distance covered by train-A is 80 kph x 1/3 hr + S-1. The total distance covered by train-B is 12.5 km (1st 15 mins) + 50/6 (next 5 mins) + S-2. Now these 2 distances are equal and = distance between the 2 stations. i.e. 80/3 + 40t = 12.5 + 50/6 + 50T; solving we get T = 7/12 hrs = 35 mins. Therefore total journey = 15 + 5 + 35 mins = 55 mins. Distance between stations = 80/3 + 40 x 7/12 km= 50 km.How did I get 12.5 km for 1st stretch for train-B? I used the formula s = ut + 1/2 at^2 (here u = 0). Hope my answers are right.

 

[addikaye03]

Ohh and most people, including many tutors found this question impossible...

I think u'll find ALOT harder Q than that, even at 2U level.

 

[untitled....]

In retrospect the qu. isnt very difficult but i guess the wording of the qu confused many people, and being one of the later qus, the midset they had kinda disadvantaged them.