Solve for t...

Question

Solve for t where

 

d= vt + at^2/2

Answer 1

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Answer 2

I suggest solving for t from the quadratic formula.

Given:  d = vt + at²/2

(1/2)at² + vt - d = 0

t ={-v ± √[v² - 4(1/2)a(-d)]} / [2(1/2)a]

t = [-v ± √(v² + 2ad)] / a

Answer 3

Subtract vt on both sides of equation.

 

d - vt = at² / 2

 

 

Multiply both sides of the equation by 2.

 

2(d - vt) = at²

 

 

Divide both sides of the equation by a.

 

[2d - 2vt)] / a = t²

 

 

Square-root both sides of the equation as the last step.