What are the velocities of the two objects when they meet?

[Amuro]

Homework Statement

Two objects A and B are moving in opposite directions toward each other in one dimensional motion along the east-west (-X, +X) line. Initially they have velocities of equal magnitude, 3.00 m/sec, with the first particle subject to a uniform acceleration of 2.00m/sec
² directed in the positive +X direction and B, which is 20.00 meters away in the +X direction from A, is subject to a uniform acceleration of 1.00 m/sec² directed in the -X direction.

Homework Equations

Obtain the distance from the initial position A of the first object and the direction of the point where they meet and the time t at which the meeting occurs.

The Attempt at a Solution

For object A I wrote: x = 3t + t²
For object B I wrote: 20 - x = 3t + .5t²

I followed my professor's example and I cross multiplied but that doesn't work here. In the problem my professor did the initial velocities were set to 0, so cross multiplying worked. Can anyone help me?

 

[gneill]

Drop the expression for x from the first equation into the second. Solve the quadratic for t.

 

[Amuro]

Thank you VERY much.

 

[Borek]

Compare

http://en.wikipedia.org/wiki/Simultaneous_equations#Substitution_method

This is one of the most basic methods of solving simultaneous equations.

 

[doby466@aol.c]

I have a problem which has a part B that states:

Also obtain the magnitudes and directions of the velocities Va and Vb respectively of the two particles at the meeting point O. How do you figure this out?

 

[gneill]

I have a problem which has a part B that states:

Also obtain the magnitudes and directions of the velocities Va and Vb respectively of the two particles at the meeting point O. How do you figure this out?

The problem states that the motions are one dimensional, so determining directions of motion shouldn't be too difficult: they're either positive or negative along the x-axis.

As for the magnitude of the velocity, what is the general relationship between position and velocity? (hint: a teensy bit of calculus).