Starting from the constant-acceleration kinematic equations, write a formula that gives xf in terms of t, xi, vf, and a.
xf
if xf is final distance...
xf=vi^t+1/2 a t^2
or
xf=vf*t/2
To derive a formula that gives the final position (xf) in terms of time (t), initial position (xi), final velocity (vf), and acceleration (a), we can start with the constant-acceleration kinematic equation:
xf = xi + v_avg * t
where xf is the final position, xi is the initial position, v_avg is the average velocity, and t is the time.
To express v_avg in terms of vf and a, we use another kinematic equation:
vf = vi + a * t
Here, vi is the initial velocity. Assuming that the object starts from rest (vi = 0), we can simplify the equation to:
vf = a * t
To find v_avg, which is the average of the initial and final velocities, we can use the formula:
v_avg = (vi + vf) / 2
Since vi = 0, this simplifies to:
v_avg = vf / 2
Now we can substitute v_avg into the first equation:
xf = xi + (vf / 2) * t
So, the formula that gives xf in terms of t, xi, vf, and a is:
xf = xi + (vf / 2) * t