randFromArray([ randomConstantMotion, randomFreefallMotion, randomFreefallMotion, randomAccelMotion, randomAccelMotion, randomAccelMotion ])() MOTION.omitted MOTION.unknown

d = u(MOTION, "d")

v_i = u(MOTION, "v_i")

v_f = u(MOTION, "v_f")

a = u(MOTION, "a")

t = u(MOTION, "t")

OMITTED = {?}

UNKNOWN = {?}

Solve for UNKNOWN. Round to the nearest tenth.

Make sure you select the proper units. You may do arithmetic with a calculator.

MOTION[UNKNOWN] UNITS[UNKNOWN]

v_f = v_i + at

v_f = u(MOTION,"v_i") + (u(MOTION,"a"))(u(MOTION,"t"))

v_f = u(MOTION,"v_f")

v_f - at = v_i

u(MOTION,"v_f") - (u(MOTION,"a"))(u(MOTION,"t")) = v_i

u(MOTION,"v_i") = v_i

\dfrac{v_f - v_i}{t} = a

\dfrac{u(MOTION,"v_f") - u(MOTION,"v_i")}{u(MOTION,"t")} = a

u(MOTION,"a") = a

\dfrac{v_f - v_i}{a} = t

\dfrac{u(MOTION,"v_f") - u(MOTION,"v_i")}{u(MOTION,"a")} = t

u(MOTION,"t") = t

d = v_f t - \frac{1}{2}at^2

d = (u(MOTION,"v_f"))(u(MOTION,"t")) - \frac{1}{2}(u(MOTION,"a"))(u(MOTION,"t"))^2

d = u(MOTION,"d")

\dfrac{d + \frac{1}{2} at^2}{t} = v_f

\dfrac{u(MOTION,"d") + \frac{1}{2}(u(MOTION,"a"))(u(MOTION,"t"))^2}{u(MOTION,"t")} = v_f

u(MOTION,"v_f") = v_f

\dfrac{d - v_f*t}{-\frac{1}{2}t^2} = a

\dfrac{u(MOTION,"d") - (u(MOTION,"v_f"))(u(MOTION,"t"))}{-\frac{1}{2}(u(MOTION,"t"))^2} = a

u(MOTION,"a") = a

0 = -\frac{1}{2}a*t^2 + v_f*t - d

By the quadratic formula:

t = \dfrac{ -v_f \pm \sqrt{ v_f^2 - 2ad } }{-a}

t = \dfrac{-u(MOTION,"v_f") \pm \sqrt{(u(MOTION,"v_f"))^2 - 2(u(MOTION,"a"))(u(MOTION,"d"))}}{-(u(MOTION,"a"))}

t = u(MOTION,"t")

d = v_i t + \frac{1}{2}at^2

d = (u(MOTION,"v_i"))(u(MOTION,"t")) + \frac{1}{2}(u(MOTION,"a"))(u(MOTION,"t"))^2

d = u(MOTION,"d")

\dfrac{d - \frac{1}{2}at^2}{t} = v_i

\dfrac{u(MOTION,"d") - \frac{1}{2}(u(MOTION,"a"))(u(MOTION,"t"))^2}{u(MOTION,"t")} = v_i

u(MOTION,"v_i") = v_i

\dfrac{d - v_i t}{\frac{1}{2} t^2} = a

\dfrac{u(MOTION,"d") - (u(MOTION,"v_i"))(u(MOTION,"t"))}{\frac{1}{2}(u(MOTION,"t"))^2} = a

u(MOTION,"a") = a

0 = \frac{1}{2} at^2 + v_i t - d

By the quadratic formula:

t = \dfrac{ -v_i \pm \sqrt{v_i^2 + 2ad} }{a}

t = \dfrac{-u(MOTION,"v_i") \pm \sqrt{(u(MOTION,"v_i"))^2 + 2(u(MOTION,"a"))(u(MOTION,"d"))}}{u(MOTION,"a")}

t = u(MOTION,"t")

d = \frac{1}{2}(v_i + v_f)t

d = \frac{1}{2}(u(MOTION,"v_i") + u(MOTION,"v_f"))(u(MOTION,"t"))

d = u(MOTION,"d")

\dfrac{2d}{t} - v_f = v_i

\dfrac{2(u(MOTION,"d"))}{u(MOTION,"t")} - u(MOTION,"v_f") = v_i

u(MOTION,"v_i") = v_i

\dfrac{2d}{t} - v_i = v_f

\dfrac{2(u(MOTION,"d"))}{u(MOTION,"t")} - u(MOTION,"v_i") = v_f

u(MOTION,"v_f") = v_f

\dfrac{2d}{v_i + v_f} = t

\dfrac{2(u(MOTION,"d"))}{(u(MOTION,"v_i")) + (u(MOTION,"v_f"))} = t

u(MOTION,"t") = t

v_f^2 = v_i^2 + 2ad

\dfrac{v_f^2 - v_i^2}{2a} = d

\dfrac{(u(MOTION,"v_f"))^2 - (u(MOTION,"v_i"))^2}{2(u(MOTION,"a"))} = d

u(MOTION,"d") = d

\pm\sqrt{v_f^2 - 2ad} = v_i

\pm\sqrt{(u(MOTION,"v_f"))^2 - 2(u(MOTION,"a"))(u(MOTION,"d"))} = v_i

u(MOTION,"v_i") = v_i

v_f = \pm\sqrt{v_i^2 + 2ad}

v_f = \pm\sqrt{(u(MOTION,"v_i"))^2 + 2(u(MOTION,"a"))(u(MOTION,"d"))}

u(MOTION,"v_f") = v_f

\dfrac{v_f^2 - v_i^2}{2d} = a

\dfrac{(u(MOTION,"v_f"))^2 - (u(MOTION,"v_i"))^2}{2(u(MOTION,"d"))} = a

u(MOTION,"a") = a