What is the final velocity?

1. Sep 28, 2011

albodibran

1. The problem statement, all variables and given/known data

a car is at a velocity of 20 km/h if the car traveled 120 km in 3 hours at constant accelration. what is the final velocity?

2. Relevant equations

3. The attempt at a solution

I am completely confused. The book does not even list the particular formula above. And not much practice examples are given . I have an issue with understanding these variables. I dont see the correlation between the variables and the particular numbers. and its making a potentially easy problem non understandable.

2. Sep 28, 2011

cepheid

Staff Emeritus
Re: Kinematics-velocity&acceleration

Welcome to PF albodibran!

In the equation you typed above, v is the current velocity (when the object is at distance d from its starting point), v0 is the initial velocity (when the object began accelerating). The variable 'a' is the acceleration (which is constant in this case) and d is the total displacement.

However, you don't need this equation. In fact, you don't even need the distance value you were given. Answer this question: what is the definition of acceleration?

Bearing in mind the definition above, if you have an acceleration value, and a time interval, what can those two things tell you about the velocity over that time interval?

3. Sep 28, 2011

Ignea_unda

Re: Kinematics-velocity&acceleration

First, welcome to PF!

Let's see if we can help get you straightened out.

If we have constant acceleration,

$V= V_0 + at (1)$

$V$ is the final velocity, $V_0$ is the initial velocity, $a$ is the acceleration, and $t$ is the time.

Also, we have the displacement,
$d = \frac{1}{2}(V + V_0) t (2)$

$d$ here, as said, is the distance traveled, also known as displacement.

If we rearrange (1) to solve for t, we get
$t = \frac{V-V_0}{a} (3)$

Now from here, just substitute (3) into (2) for t. You then have:
$d = \frac{1}{2}(V + V_0) (\frac{V-V_0}{a})$

When you work out your multiplication (I hope you're verifying what I'm doing here, it'll help) and rearrange things,

$V^2 = V_0^2 + 2ad$

Does that help you to see where they are coming from? If not, let us know and we'll see what we can do for you.

4. Sep 28, 2011

albodibran

Re: Kinematics-velocity&acceleration

I figured that out thank you I will post a issue I have with part of another problem