What should be the formula to solve this?

1. Sep 7, 2011

rexkhyz29

This is the given problem:

Cars A and B approach each other on a straight road from points 457 m apart. A has an initial velocity of 20 m/s and is decelarating at the rate of 0.4 m/s². B has an initial velocity of 5 m/s and is accelerating at the rate of 0.3 m/s². When will the cars meet and how far will car A have travelled?

note: this is not homework guys. I just want to recall my physics. Thanks in advance.

2. Sep 7, 2011

Staff: Mentor

Last edited by a moderator: Apr 26, 2017
3. Sep 7, 2011

rexkhyz29

1. The problem statement, all variables and given/known data

Cars A and B approach each other on a straight road from points 457 m apart. A has an initial velocity of 20 m/s and is decelarating at the rate of 0.4 m/s². B has an initial velocity of 5 m/s and is accelerating at the rate of 0.3 m/s². When will the cars meet and how far will car A have travelled?

2. Relevant equations

none

3. The attempt at a solution[/b

The formula I do know for the problem is
Da + Db = 457
Da = Vit + at²
2

and..

Db= Vit + at²
2

is this right? if it is, then what is the next step to solve this? thanks in advance.

4. Sep 7, 2011

rexkhyz29

Uniform Acceleration:

vave=(vi+vf)/2

is this the formula i should use? if it is. Can you explain to me how to solve this kind of problem? I only just need a guide not the exact answer.

5. Sep 7, 2011

Staff: Mentor

The first thing to do in these sorts of problems is to choose a coordinate system, then taking that coordinate system into account, assign values to all the constants in your equations of motion for the two bodies. Be careful with the signs of the values! They should correspond to what is happening in the coordinate system (The prose description can be a bit lax on specifying the signs that should be assigned to values, expecting the reader to sort it out by context).

Use the 'complete' version of the equation of motion for constant acceleration for both bodies:
$$x = x_o + v_o t + \frac{1}{2}a t^2$$

What values will you assign to the constants for each body?

6. Sep 7, 2011

Staff: Mentor

I'd use the formula for displacement & time:
$$x = x_0 + v_0 t + (1/2) a t^2$$
Hints: Let x0 = 0 for car A, thus x0 = 457 for car B.
If car A's initial velocity v0 is +20 m/s, what would car B's initial velocity be?