# Homework Help: Acceleration word problem help!

1. Sep 10, 2006

### kholdstare121

I'm taking highschool physics right now, and we're doing kinematics in one dimension.
Well I've been stuck on this word problem for days and stumbled accross this
Thought maybe you could help. Anyway it is:
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Two soccer players start from rest, 48m apart. They run directly toward each other, both players accelerating. The first player has an acceleration whose magnitude is 0.50 m/s^2. The second player's acceleration has a magnitude of 0.30 m/s^2.
(a) How much time passes before they collide?
(b)At the instant they collide, how far has the first player run?
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I've tried to tackle this as any other algebra distance=rate*time problem (but with some physics equation involved)
I attempted to get the final velocity of both runners by using the equation
Vf^2=vi^2+at
where vf=final velocity and vi=intitial.
I used '48m' as the value for distance when I did this
Then when I get my final velocity I'd figure out the average velocity for both runners.
Then tackle the problem by adding their individual rate*time together to get rt(of the first guy)+rt(second guy)=48m ,Attempting to get the time they collide from that.
BUT, apparently by plugging in 48m in the physics equation gave me a bad final velocity, therefore a bad time.
I know the correct answer for part a is 11 seconds, but don't know how it's obtained. Please I would be greatful if anyone could help.
I'll also try to clear this up if anyone's confused.
Thanks.

Last edited: Sep 10, 2006
2. Sep 10, 2006

### Israfil

solution

Hey :)

Both players are accelerating, so the equation for both their movement is
first player s_1 = 1/2*a_1*t^2
2nd player s_2 = 1/2*a_2*t^2
with a_1 = 0.5 m/s^2 and a_2 = 0.3 m/s^2
you know that s_1 + s_2 = 48m

Now you sum up both players' equations and recieve:
s_1 + s_2 = 1/2*t^2*(a_1+a_2) where t is the only onknown, so you get t!

Then just insert the value of t in the first player's equation and you'll get s_1 which answers the 2nd question.

have fun :)

3. Sep 10, 2006

### kholdstare121

Oh wow!
I feel REALLY dumb right now.
Was the solution that simple?
I just worked it out and got the right answer(so it is that simple :rofl: )
I was going through every other equation, missing the easy connection with this one.
Thanks a lot

4. Sep 1, 2008

### pandabento09

Re: solution

I'm completely lost. so it would be s1+s2= 1/2t^2 (0.5 +0.30) ???
48 = 1/2 t^2 (0.5 +0.39)
what did i do wrong/?

Last edited: Sep 1, 2008
5. Sep 1, 2008

### Redbelly98

Staff Emeritus
That looks correct (other than it's 0.30, not 0.39, for one of the accelerations).

If I were setting this up, I would have started by writing

0 = 48 - 1/2 t^2 (0.5 +0.30),

which results in the same thing.