MHB Why is the no v kinematic equation helpful for solving kinematics problems?

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The no v kinematic equation, expressed as x = x₀ + v₀t + (1/2)at², is designed for scenarios where the final velocity is unknown. It is clarified that there is no specific requirement to evaluate the (1/2)at² term first; calculations can be performed in any order. The term "no v kinematic equation" refers to its use when the final velocity is not a factor in the problem. Understanding the four kinematic equations helps students identify which variable is missing and simplifies the algebra involved in solving kinematics problems. This approach allows for more straightforward problem-solving without needing to substitute between equations.
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In the no v kinematic equation, $x={x}_{o}+{v}_{o}t+a{t}^{2}/2$, why do you have to solve $a{t}^{2}/2$ first before solving down completely?
 
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Hello and welcome to MHB! (Wave)

What do you mean by "solve $at^2/2$ first?"
 
Since t has the power of 2 for the acceleration, perhaps this is why the OP has stated "first" . . .?
Also, jsspoon, is there any specific question regarding the kinematic equation?
 
If by "solve" you simply mean "evaluate x for a given value of t", you do not need to evaluate [math]\frac{1}{2}at^2[/math]. You can do the calculations in any order. If you mean "solve for t for a given value of x", again there is nothing special about the [math]\frac{1}{2}at^2[/math] term- you can use the quadratic formula to solve.

And why was this called "no v kinematic equation"?
 
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HallsofIvy said:
If by "solve" you simply mean "evaluate x for a given value of t", you do not need to evaluate [math]\frac{1}{2}at^2[/math]. You can do the calculations in any order. If you mean "solve for t for a given value of x", again there is nothing special about the [math]\frac{1}{2}at^2[/math] term- you can use the quadratic formula to solve.

And why was this called "no v kinematic equation"?

The OP'er was one of my students, and we had labels for the four kinematic equations:
\begin{align*}
y&=y_0+v_{0y}t+a_y t^2/2 \qquad \text{no }v_y \\
\Delta y&=(v_y+v_{0y})t/2 \qquad \text{no }a_y \\
v_y&=v_{0y}+a_y t \qquad \text{no }y \\
v_y^2&=v_{0y}^2+2a_y \Delta y \qquad \text{no }t.
\end{align*}
Since, in kinematics, there are basically four players: $y, v_y, a_y, t$, there's one kinematic equation corresponding to which kinematic variable is missing. Knowing these four equations helps the students with the algebra, because they can just solve the one they need, and not necessarily have to plug one equation into another.
 
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