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 Kinematic Equations
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.

roundTo(1, MOTION[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

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

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

u(MOTION,"a") = a

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

\frac{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")

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

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

u(MOTION,"v_f") = v_f

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

\frac{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

t = \frac{ -v_f +- \sqrt{ v_f^2 - 2ad } }{-a}

t = (-u(MOTION,"v_f") +- 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")

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

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

u(MOTION,"v_i") = v_i

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

\frac{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

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

t = \frac{-u(MOTION,"v_i") +- 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")

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

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

u(MOTION,"v_i") = v_i

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

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

u(MOTION,"v_f") = v_f

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

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

u(MOTION,"t") = t

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

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

u(MOTION,"d") = d

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

u(MOTION,"v_i") = v_i