How Do a Car and Truck Meet When Starting at Different Times?

[link107]

Homework Statement

A truck starts from rest and accelerates at 0.9m/s2. 0.8s later, a car accelerates from rest at the same starting point with an acceleration of 2.5m/s2

Where and when does the car catch the truck?

Homework Equations

Motion equations

Xf-Xo=Vox(t)+1/2(a)(t)^2

The Attempt at a Solution

x truck=x car

1/2(a)(t)^2=1/2(a)(t-0.8s)^2
1/2(a)(t)^2=1/2(a)(t^2-1.6t+0.64)
1/2(0.9)t^2=1/2(2.5)(t^2-1.6t+0.64)
0.45t^2=1.25t^2-2t+0.8
0.8t^2-2t+0.8t=0
quadratic equation =

2+1.2/1.6=2s
2-1.2/1.6=0.5s

I don't know where I went wrong but the value for time isn't working for me. The assignment continues to say the answer is incorrect... Please help me pin point my error so I can correct myself.

Thank you

[/B]

 

[Brian T]

I would try to redo the algebra. Perhaps cancel out 1/2 on both sides to make things less messy

Edit: your math looks right. Plug in 2s into the equation, it works. Now plug in .5s, hopefully you notice something.

Always check your answer to see if they make mathematical sense and physical sense.

 

[link107]

Well to start, there can't be two positive time answers. Once the car passes the truck, they will never meet again (since the car contonues to accelerate faster)

I would try to redo the algebra. Perhaps cancel out 1/2 on both sides to make things less messy

I already canceled them out and still got the same results... It doesn't work still.

 

[Rellek]

Hey, do you know how this equation is derived? If you work this in the integral form you might see what you did wrong.

 

[link107]

Hey, do you know how this equation is derived? If you work this in the integral form you might see what you did wrong.

The thing is we didn't learn integral form yet so I don't know how I would do it.

 

[Rellek]

Well, ok.

Judging from your work, it seems as if you wanted to keep the time constant with respect to the first car to start. There's nothing wrong with this. However, if this is the case, your work is saying that the two cars will be meeting each other at different times with respect to the first car. Namely, you are saying that car 2 is going to come in contact with the first car .8 seconds earlier than car 1 comes in contact with car 2. How could they come in contact at different times? They should come in contact at the exact same ending time T.

 

[link107]

Well, ok.

Judging from your work, it seems as if you wanted to keep the time constant with respect to the first car to start. There's nothing wrong with this. However, if this is the case, your work is saying that the two cars will be meeting each other at different times with respect to the first car. Namely, you are saying that car 2 is going to come in contact with the first car .8 seconds earlier than car 1 comes in contact with car 2. How could they come in contact at different times? They should come in contact at the exact same ending time T.

How could I set the equation in that case? should I set both cars (t-0.8)^2?

 

[link107]

Ill just ask my teacher tomorrow, thank you guys.

 

[Rellek]

It looks correct actually