What should be the formula to solve this?

[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.

 

[Doc Al]

A list of kinematic formulas can be found here: https://www.physicsforums.com/showpost.php?p=905663&postcount=2"

Find expressions for the position of each car (measured from the same point) as a function of time. Then you can solve for when they meet by setting those positions equal.

 

[rexkhyz29]

Homework Statement

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?

Homework 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.

 

[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.

 

[gneill]

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?

 

[Doc Al]

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?