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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Catch/Overtake Problems concept. You can view video lessons to learn Catch/Overtake Problems. Or if you need more Catch/Overtake Problems practice, you can also practice Catch/Overtake Problems practice problems.

What textbook is this problem found in?

Our data indicates that this problem or a close variation was asked in Fundamentals of Physics - Halliday Calc 10th Edition. You can also practice Fundamentals of Physics - Halliday Calc 10th Edition practice problems.