# Velocity and acceleration of two objects

1. Sep 15, 2007

### strigner

1. The problem statement, all variables and given/known data
A car is travelling on cruise control at velocity v1. Ahead on the road, a distance x away, a truck is travelling at a slower constant velocity v2. What is the maximum constant acceleration the car needs to avoid hitting the truck?

2. Relevant equations

3. The attempt at a solution

The only thing I could think of solving was the time when they would collide. So I wrote like this:

v2*t + x = v1*t

x = t(v1 - v2)

t= x/(v1-v2)

I'm not sure if this is the right way to start the problem and if it is I don't know where I can go with this.

2. Sep 15, 2007

### bob1182006

there is one equation you are missing,

$$V_x^2=V_{0x}^2+2a_x\triangle x$$

you can derive it from the equation of the position of a particle:
$$\triangle x = v_{0x}t+1/2at^2$$

and the velocity of a particle

$$V=V_{0x}+at$$

Solve the velocity equation for t, plug it into the equation for the position of a particle and you get that equation.

Back to the problem:

right now say neither car/truck accelerated/decelerated, will they hit each other?
try and determine some relationship between v1 and v2, what words does the problem use that gives you some relationship between v1 and v2?

The car will be going from velocity v1 to what? what velocity will it need at least to not hit the truck?
Once you have that use the equation to determine the acceleration that will be needed for the car. and be sure to make sure you have the sign right, will the car accelerate? or decelerate?