Physics question!?

Question

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

Answer 1

v(t)=v0-a*t
and
x(t)=v0*t-.5*a*t^2

from
0 x(2)=40=v0*2-.5*a*4

for the second
x(4.4)=80=v0*4.4-.5*a*4.4^2

solve for a and v0

20+a=v0
80/4.4+a*2.2=v0

80/4.4+a*2.2=20+a

a=(20-80/4.4)/1.2
a=8/5.28

v0=113.6/5.28

now solve for t when v(t)=0

recall
v(t)=v0-a*t
113.6/5.28=8*t/5.28
t=113.6/8
t=14.2 seconds

recall
x(t)=v0*t-.5*a*t^2

x(14.2)=113.6*14.2/5.28-
.5*8*14.2^2/5.28

=152.76

or 7.64 carriages

there are 8 carriages.


j

Answer 2

I worked it out to be 8 carts like the other answerers.

Total distance after the train stops is 152.758m, therefore divide that by 20m/cart and you'll get 7.638carts, or 8 carts.

Things you should think about;

1. You don't have initial speed of train (u).
2. You have a constant acceleration (a).
3. You have time (t) it takes with respect to distance (s) travelled. These are constants with respect to the carts in question.

a] Work out u for the first two carts in terms of a.
b] Using u in terms of a from a], use it to find a for the next two carts. Since both share a and u.
c] With a found numerically, use this to find u from a].
d] All what's left is to find out the total distance before the train stops. Final speed is v and that's obviously 0. You have initial speed of train u and you have the acceleration a (should be negative because train is decelerating). Use an appropriate formula to find total distance. (hint: no need to consider time).

The tricky thing about this question is building the model in your head. You should think of the student moving and not the train. Alternative way is to imagine of the student decelerating and passing 20m tiles on the floor.

Answer 3

8

Answer 4

I worked it out independently, but much the same way as "odu83", and got exactly the same answer. So I think he and 8 are right!

Answer 5

Your question is unanswerable

Answer 6

Four, I would guess.

Answer 7

7,632