Mechanics/Calculus question phrasing help

[maximade]

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?
Thanks in advance.

 

[issacnewton]

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..

 

[maximade]

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?

 

[issacnewton]

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

 

[paranormal]

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!