How Do You Calculate Final Velocity with Constant Acceleration?

[albodibran]

Homework Statement

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?

Homework Equations

V^2=Vo^2+2ad

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 don't see the correlation between the variables and the particular numbers. and its making a potentially easy problem non understandable.

please help

 

[cepheid]

Welcome to PF albodibran!

Homework Statement

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?

Homework Equations

V^2=Vo^2+2ad

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 don't see the correlation between the variables and the particular numbers. and its making a potentially easy problem non understandable.

please help

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?

 

[Ignea_unda]

First, welcome to PF!

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

If we have constant acceleration,

[itex] V= V_0 + at (1)[/itex]

[itex]V[/itex] is the final velocity, [itex]V_0[/itex] is the initial velocity, [itex]a[/itex] is the acceleration, and [itex]t[/itex] is the time.

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

[itex]d[/itex] here, as said, is the distance traveled, also known as displacement.

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

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

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

[itex]V^2 = V_0^2 + 2ad[/itex]

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.

 

[albodibran]

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

 

[rwisz]

The final velocity is the velocity of the car at the end of its journey. In this case, the car has traveled 120 km in 3 hours at a constant acceleration. We can use the formula V^2=Vo^2+2ad to calculate the final velocity, where V is the final velocity, Vo is the initial velocity (20 km/h in this case), a is the acceleration, and d is the distance traveled (120 km in this case).

Substituting the values into the formula, we get:

V^2 = (20 km/h)^2 + 2(a)(120 km)

V^2 = 400 km^2/h^2 + 240a km

To solve for V, we need to know the acceleration of the car. This information is not provided in the problem, so we cannot determine the final velocity with the given information. The book may have not listed this formula because it requires more information (such as the acceleration) to solve the problem.

In general, the final velocity can be calculated using the formula V = Vo + at, where V is the final velocity, Vo is the initial velocity, a is the acceleration, and t is the time. However, since we do not have the acceleration in this problem, we cannot use this formula either. It is important to make sure all necessary information is provided in order to solve a problem accurately.