# Mechanics/Calculus question phrasing help

In summary, the conversation discusses deriving the kinematic equations for constant acceleration from the given equations for change in position and change in velocity. The equations used are v=v(o)+at and x=V(avg)t, and the goal is to manipulate them to eliminate variables and get equations in terms of x, v(o), a, and t.

## Homework Statement

Derive the kinematic equations for constant a from change in x=V(avg)Xt & change in v= a(avg)Xt

## Homework Equations

v=v(o)+at
(Every other equation that can be made from x=x(1)+V(0)t+.5at^2)
x= position
a=acceleration (constant)
v=velocity
t=time

## The Attempt at a Solution

My main problem with this problem is that I don't know exactly what it's asking and the phrasing confuses me.
But what I did was turned the change in x=V(avg)Xt into v=v(o)+at through deriving and substitution.
For the change in v= a(avg)Xt equation, I turned it into a=change in v/t through deriving and substitution.
Once again I'm not even sure that I even answered the question, can someone please interpret the question in a way I can understand it?

hi max

since the acceleration is constant, $$\inline{a_{avg}=constant=a}$$
and the equations you are supposed to use are $$\inline{x=V_{avg}t}$$ and
$$\text{change in v}=a_{avg}t=at$$

now remember that

$$V_{avg}=\frac{V+V_o}{2}$$

and change in V=final velocity - initial velocity = $V-V_o$

so use these equations , manipulate them...

for example... $\text{change in v}=V-V_o = at$
so $V=V_o +at$ this would be one of the equations of kinematics for the constant
acceleration..

Last edited:
Hi Issac, I know how to manipulate the equations and such, my main problem is that I don't know what the question itself is asking. Like am I supposed to find a= through the 2 equations?

there are 3 main equations of the kinematics for the constant acceleration ... i already showed you one of them...now to get the second equation, you need to eliminate V and get an equation in x, V_o ,a and t... do it

Hi there,

It looks like you are on the right track with your attempt at a solution. The homework statement is asking you to derive the kinematic equations for constant acceleration from the given equations for change in position and change in velocity. These equations are given as:

change in x = average velocity x time
change in v = average acceleration x time

To derive the kinematic equations, you need to use the definition of average velocity and average acceleration, which are:

average velocity = change in x / time
average acceleration = change in v / time

By rearranging these equations and substituting them into the given equations, you should be able to derive the kinematic equations:

v = v0 + at
x = x0 + v0t + 1/2at^2
v^2 = v0^2 + 2a(x-x0)

Where:
v = final velocity
v0 = initial velocity
x = final position
x0 = initial position
a = acceleration
t = time

I hope this explanation helps clarify the question for you. Keep up the good work!

## 1. What is the difference between mechanics and calculus?

Mechanics is a branch of physics that deals with the study of motion and the forces that cause it, while calculus is a branch of mathematics that deals with the study of change and motion. Mechanics uses calculus to describe and analyze the motion of objects.

## 2. How is calculus used in mechanics?

Calculus is used in mechanics to describe and analyze the motion of objects. It helps us to understand how objects move and how forces affect their motion. Calculus allows us to calculate important quantities such as velocity, acceleration, and force.

## 3. What is the difference between kinematics and dynamics?

Kinematics is the branch of mechanics that deals with the motion of objects without considering the causes of motion, while dynamics is the branch that deals with the forces that cause motion. In other words, kinematics describes how objects move, while dynamics explains why they move.

## 4. How do you approach a mechanics/calculus problem?

The first step in approaching a mechanics/calculus problem is to carefully read and understand the problem. Then, identify the known and unknown quantities, and determine which equations and concepts are relevant to the problem. Next, use calculus to solve for the unknown quantities and make sure to check your answer for accuracy.

## 5. How can I improve my understanding of mechanics and calculus?

To improve your understanding of mechanics and calculus, it is important to practice solving problems and to seek help when needed. It can also be helpful to visualize the concepts and to relate them to real-world situations. Additionally, staying organized and reviewing the fundamental concepts regularly can also improve understanding.

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