# Homework Help: Kinematics - Motion along a straight line

1. Sep 29, 2006

### SA32

I’m having difficulty with an assignment for my Physics class.

Here’s the question:

“Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance $$D_{A}$$ beyond the starting line at t = 0. The starting line is at x = 0. Car A travels at a constant speed $$v_{A}$$. Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed $$v_{B}$$, which is greater than $$v_{A}$$.

How long after Car B started the race will Car B catch up with Car A?
Express the time in terms of given quantities.”

My embarrassingly unsuccessful attempt:
My thinking was that, when Car B catches Car A, $$x_{A} = x_{B}$$.

I substituted the given quantities for Car A and Car B separately into the equation,
$$x = x_{o} + v_{ox}(t-t_{o}) + \frac{1} {2}*a_{x}(t-t_{o})^2$$

where:
x = position as a function of time
xo = initial position
vox = initial velocity
t = a certain time
to = initial time
ax = acceleration

For Car A, I got (simplified):
$$x = D_{A} + v_{A}(t)$$

For Car B, I got (also simplified):
$$x = v_{B}(t)$$

Equating them, $$D_{A} + v_{A}(t) = v_{B}(t)$$, and solving for t, I got:
$$\frac{v_{B}t - D_{A}} {v_{A}} = t$$

Which is incorrect.

I know I shouldn’t have “t” on the left side, but other than that I’m completely lost and would really appreciate it if anyone could point me in the right direction.

Last edited: Sep 29, 2006
2. Sep 29, 2006

### SA32

Having issues fixing the fraction in my answer, so I'll try again here.

Here is what I got:

$$\frac{v_{B}t - D_{A}} {v_{A}} = t$$

3. Sep 30, 2006

### Hootenanny

Staff Emeritus
It may be easier to consider thier relative velocity ($v_{r} = v_{B}-v_{A}$).

4. Sep 30, 2006

### SA32

Thanks a bunch, got the answer!

5. Oct 1, 2006

### sunbunny

I have the same question with the cars. I've made car A equal to car B and was able to get this equation:

Da + va(t) = vb(t) and then i subtracted va(t) and then took out the common factor of t like so:

Da= t(vb-va)

then found that t= Da/(vb-va)

I'm not sure if this is the right equation, i'm pretty sure it's not so if anyone can help me that would be great!

6. Oct 2, 2006

### Hootenanny

Staff Emeritus