# Linear motion

1. Nov 2, 2006

### Parallel

hello

I'm having some trouble with the following problem:

train B leaves point A at 8am to point B located 30 km straight a head.
the train has constant acceleration a=0.05 m/sec^2

now train B leaves point B 5 minutes before train A gets there,what is the acceleration of train B in order for the trains to meet with the same velocity?
(i.e will not collide)

I computed the speed of train A 5 min before it arrived to point B.
I know it's acceleration,but it seems I dont have enough information to solve the problem,I have 2 unknowns: train B's acceleration and the location they meet...but I have only one equation.

2. Nov 2, 2006

### stunner5000pt

what is the initial velocity of A. What is its acceleration?
what would be its velocity at some t while it travelling along the track???
Write an equation using the above knowns and unknowns

Do the smae thing for B. BUT DONT USE THE SAME SYMBOLS or you will get confused. (use differetn subscripts). Keep in mind the time it took for train B to reach a velocity is different for the time it took train A to reach that velocity.

Do that first

3. Nov 2, 2006

### Parallel

this is what I have.

for train A,i'll set the initial velocity as the velocity 5 min before it gets point B,it's 39 m/s

so: Va = 39 + 0.05t

for train B,I assume it starts from rest so:

Vb = at

I can equate them,but as I said before,I only have one equation and 2 unknowns.

I really can't figure this out,I spent like an hour on this problem,but couldn't come up with anything

4. Nov 2, 2006

### stunner5000pt

thats good

now consider that distance in which they may meet

if A convered a distance d, then what distance has B covered in the same amount of time??

5. Nov 2, 2006

### Parallel

I'm not following you.
I can't understand how this helps me,with solving the equation.

but the distance is speed*time.

or should I use:
x = x0 + v0t + 0.5at^2
?

6. Nov 2, 2006

### arildno

It is certainly best to set up the similar equations for the POSITIONS, and use those to solve the problem

7. Nov 2, 2006

### Parallel

but even with the positions,I get 2 unknowns.

I dont know where they meet,and I dont know the acceleration of train B.

8. Nov 2, 2006

### arildno

First, you should write down the position functions for each train:
$$x_{A}(t)=x_{A,0}+v_{A,0}t+\frac{a_{A}t^{2}}{2}$$
$$x_{B}(t)=x_{B,0}+v_{B,0}t+\frac{a_{B}t^{2}}{2}$$

where:
$$x_{A,0}=x_{A}(0), x_{B,0}=x_{B}(0), v_{A,0}=v_{A}(0), v_{B,0}=v_{B}(0)$$
Do you agree with this?

Now, you need to define what your spatial and temporal origin should be, before trying to determine the various quantities involved.