Math/Physics Problem?

Question

Given the equations x= x(sub 0) + v(sub 0)Xt + 1/2XaXt^2 and v= v(sub 0) + aXt (where the capital X means multiplied by) show that an expression for v that has no explicit dependence on time (i.e. the variable t does not appear in the equation) can be written as v = SquareRoot of V(sub 0)^2 + 2XaX(x-x(sub 0))

Answer 1

x=x0+v0*t+.5*a*t^2

v=v0+a*t
t=(v-v0)/a

plug into equation for x
x=x0+v0*(v-v0)/a+
.5*a*(v-v0)^2/a^2

simplify
2*a*x=
2*a*x0+
2*v0*v-2*v0^2+
v^2-2v*v0+v0^2

simplify more

v=sqrt(2*a*(x-x0)+v0^2)

note that * means multiplied by

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