How Do You Calculate When One Moving Object Overtakes Another?

[kittykatxox]

kinematics question help please :)?

So I've tried to attempt this problem by finding possible things like time or velocity but it just does not come out right. Help is greatly appreciated :)

Problem:

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.0 m/s^2. At the same instant a truck is 13.4 m down the road and traveling with a constant speed of 9.3 m/s. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be traveling at that instant?

heres some work I did:
Truck:
v=x/t
9.3=13.4/t
t= 1.44 sThanks :)

 

[N-Gin]

If you know how far are the truck and the car from the traffic light at any moment, this problem is easy to solve.

So, for the car you have

$$x(t)=\frac{1}{2}at^2.$$

And for the truck

$$x(t)=x_0+vt.$$

Now you just need to figure what is $x_0$ and what is the condition for the car and the truck to meet.

 

[kittykatxox]

What is x(t)?

 

[N-Gin]

What is x(t)?

$x(t)$ is the function with $t$ as a variable. It tells you what is the distance $x$ from the traffic light at the time $t$.