I’m having difficulty with an assignment for my Physics class.(adsbygoogle = window.adsbygoogle || []).push({});

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 [tex]D_{A}[/tex] beyond the starting line at t = 0. The starting line is at x = 0. Car A travels at a constant speed [tex]v_{A}[/tex]. Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed [tex]v_{B}[/tex], which is greater than [tex]v_{A}[/tex].

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, [tex]x_{A} = x_{B}[/tex].

I substituted the given quantities for Car A and Car B separately into the equation,

[tex]x = x_{o} + v_{ox}(t-t_{o}) + \frac{1} {2}*a_{x}(t-t_{o})^2[/tex]

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):

[tex]x = D_{A} + v_{A}(t)[/tex]

For Car B, I got (also simplified):

[tex]x = v_{B}(t)[/tex]

Equating them, [tex]D_{A} + v_{A}(t) = v_{B}(t)[/tex], and solving for t, I got:

[tex]\frac{v_{B}t - D_{A}} {v_{A}} = t[/tex]

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.

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# Homework Help: Kinematics - Motion along a straight line

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