How do I derive the equation vf^2=vi^2+2ad using vf=vi+at and d=vi*t+(at^2)/2?

Question

How do I derive the equation vf^2=vi^2+2ad using vf=vi+at and d=vi*t+(at^2)/2?

Answer 1

To derive this, you need to eliminate time from the given equations.  Start with

 

v_f = v_i + at ⇒ t = (v_f - v_i)/a

 

Plug this expression for t into 

 

d = v_it + at²/2

 

and get

 

d = v_i(v_f - v_i)/a + a[(v_f - v_i)/a]²/2

 

Multiply both sides by 2a and get

 

2ad = 2v_iv_f - 2v_i² + (v_f² - 2v_iv_f + v_i²)]

 

2ad = v_f² - v_i²

 

v_f² = v_i² + 2ad