Question

which equation from the kinematic list below would be best if you know an objects initial velocity, acceleration, and time, and you want to find displacement?
$v_f = v_i + at$
final velocity equals initial velocity plus acceleration times time.
$x = v_i t + \frac{1}{2}at^2$
displacement equals initial velocity times time plus one half acceleration times time squared.
$v_f^2 = v_i^2 + 2ax$
final velocity squared equals initial velocity squared plus two times acceleration times displacement.
$f = ma$
force equals mass times acceleration

Explanation:

Step1: Analyze the first equation

The equation \(v_f = v_i+at\) is used to find the final velocity \(v_f\), not displacement \(x\).

Step2: Analyze the second equation

The equation \(x = v_it+\frac{1}{2}at^{2}\) has \(x\) (displacement) as the subject, and it uses \(v_i\) (initial velocity), \(a\) (acceleration) and \(t\) (time) which are the known quantities.

Step3: Analyze the third equation

The equation \(v_f^{2}=v_i^{2}+2ax\) is used when final velocity \(v_f\) is involved in the problem, and it is not straightforward to solve for \(x\) when \(v_f\) is unknown.

Step4: Analyze the fourth equation

The equation \(F = ma\) is from Newton's second law and is related to force, mass and acceleration, not kinematics for displacement.

Answer:

Displacement equals initial velocity times time plus one - half acceleration times time squared (\(x = v_it+\frac{1}{2}at^{2}\))