Whether equations work to describe motion

[PAstudent]

Homework Statement

An object moves along the x-axis according to the position function x=At^2-Bt+C, where x is in meters and t in seconds; A,B, C are constants. Explain why or why not the equations v^2= vo^2+2a(x-xo) and v average= 1/2(v+vo) can be used to describe the motion of the object. Using mathematics is recommended[/B]

Homework Equations

The Attempt at a Solution

So, the first one would be possible because it is describing a constant acceleration equation and since it is only a polynomial of degree 2 the acceleration would be constant. Also, you can find the velocity by taking the 1st derivative and the acceleration is the second derivative. The second equation is wrong because average velocity is displacement over change in time.

 

[Chestermiller]

Homework Statement

An object moves along the x-axis according to the position function x=At^2-Bt+C, where x is in meters and t in seconds; A,B, C are constants. Explain why or why not the equations v^2= vo^2+2a(x-xo) and v average= 1/2(v+vo) can be used to describe the motion of the object. Using mathematics is recommended[/B]

Homework Equations

The Attempt at a Solution

So, the first one would be possible because it is describing a constant acceleration equation and since it is only a polynomial of degree 2 the acceleration would be constant. Also, you can find the velocity by taking the 1st derivative and the acceleration is the second derivative. The second equation is wrong because average velocity is displacement over change in time.

The average velocity is the change in displacement over the change in time. If you evaluate that, you will find that the second equation is correct.

Chet

 

[PAstudent]

I just don't understand what there is to evaluate . Because I thought avg velocity was x2-x1/t2-t1

 

[Chestermiller]

I just don't understand what there is to evaluate . Because I thought avg velocity was x2-x1/t2-t1

$x_2-x_1=At^2-Bt$
$t_2-t_1=t$
Average velocity = $At-B$
$v_0 = -B$
$v=2At-B$
Average velocity = $\frac{v_0+v}{2}=At-B$
So what can you say about the second equation in this situation? Does it give the correct average velocity or not?

Chet