So, I have to solve for 't' in this equation:

x=x_{0}+v_{0}t+1/2at^{2}

And, I can't deal with it. Somebody help?

Guest Jul 23, 2017

#1**+1 **

It's a quadratic in t.

Rewrite it as 1/2at^{2} +v_{0}t+x_{0}-x=0

Multiply by 2/a: t^{2} +(2v_{0}/a)t +2(x_{0}-x)/a = 0

Use the quadratic formula:

t = { -(2v_{0}/a) + sqrt[ (2v_{0}/a)^{2} - 4*2(x_{0}-x)/a) ] }/2 → { -v_{0} + sqrt[ v_{0}^{2} - 2a(x0-x) ] }/a

(Because t is almost certainly time here, we don't need to look at the other solution)

Alan
Jul 23, 2017

#1**+1 **

Best Answer

It's a quadratic in t.

Rewrite it as 1/2at^{2} +v_{0}t+x_{0}-x=0

Multiply by 2/a: t^{2} +(2v_{0}/a)t +2(x_{0}-x)/a = 0

Use the quadratic formula:

t = { -(2v_{0}/a) + sqrt[ (2v_{0}/a)^{2} - 4*2(x_{0}-x)/a) ] }/2 → { -v_{0} + sqrt[ v_{0}^{2} - 2a(x0-x) ] }/a

(Because t is almost certainly time here, we don't need to look at the other solution)

Alan
Jul 23, 2017