In this problem, we're asked to determine **displacement** and **final speed** at the time when the two objects meet.

This is a problem about one object catching up to another (“meet and catch” type problem).

To solve meet-and-catch type problems, we’ll always *organize what we know* about the problem, then **follow these steps**:

__Write the__for each object using UAM equation (3).**position equation**- Set the position equations
__equal to each other__. - Solve for
.**time** - (If needed) Plug the
**time**__back into another equation__to solve for*x*or*v*.

Since we’re not given information about gravity acting on either of them, we can assume they’re both traveling horizontally. We’re also given that they *both have constant acceleration* (in this case, one of the accelerations is zero), meaning we can **use the UAM equations**. Recall that the four UAM equations are:

$\overline{){\mathbf{}}{\mathbf{\left(}}{\mathbf{1}}{\mathbf{\right)}}{\mathbf{}}{\mathbf{}}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathit{a}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}\mathbf{}{\mathbf{\left(}}{\mathbf{2}}{\mathbf{\right)}}{\mathbf{}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{\left(}}\frac{{\mathbf{v}}_{\mathbf{f}}\mathbf{+}{\mathbf{v}}_{\mathbf{0}}}{\mathbf{2}}{\mathbf{\right)}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}\mathbf{}{\mathbf{\left(}}{\mathbf{3}}{\mathbf{\right)}}{\mathbf{}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{+}}{\frac{1}{2}}{\mathit{a}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}\mathbf{}{\mathbf{\left(}}{\mathbf{4}}{\mathbf{\right)}}{\mathbf{}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathit{a}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{}}}$

In this problem, we’re *directly* given two pieces of information: the constant acceleration of the automobile, *a*_{A}* *= 2.2 m/s^{2}, and the constant velocity of the truck, *v*_{T} = 9.5 m/s.

There's also some information that the problem *implies*: that the truck and auto are both at *x *= 0 at the instant the traffic light turns green (which we’ll say is *t *= 0); the auto **starts** moving at that instant, so its initial velocity *v*_{0}* _{A}* = 0; the truck is moving at a constant velocity, so

Let's organize our **target**, **known**, and unknown variables for the two vehicles:

For the truck:

i. **a**** = a_{T} = 0**

ii.

iii.

iv.

v.

For the car:

i. **a**** = a_{A} = 2.2 m/s**

ii.

iii.

iv.

v.

vi.

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.2 m/s^{2}. At the same instant a truck, traveling with a constant speed of 9.5 m/s, overtakes and passes the automobile.

(a) How far beyond the traffic signal will the automobile overtake the truck?

(b) How fast will the automobile be traveling at that instant?