Question

1. Eliminate 't' by substitution method
v)vf = vi + at ; s = vit +1/2 at²​

Answer 1

Step-by-step explanation:

Eliminate 't' by substitution method

v)vf = vi + at ; s = vit +1/2 at²

Answer 2

Answer:  $s=\frac{v_{f} ^{2} - v_{i} ^{2}}{2a}$

Step-by-step explanation:

Given: $v_{f} = v_{i} + at$  ----- (1)

          $s = v_{i}\,t + \frac{1}{2}a t^{2}$  -------(2)

We are expected to eliminate the 't' by substitution method,

Consider the equation (1)

          $v_{f} = v_{i} + at$

Let us simplify the above equation for 't',

          $at = v_{f} - v_{i}$

          $t = \frac{v_{f} - v_{i}}{a}$      -------(3)

Substitute (3) in (2) we get,

         $s = v_{i} (\frac{v_{f} - v_{i}}{a})+ \frac{1}{2} a (\frac{v_{f} - v_{i}}{a})^{2}$

         $s = v_{i} (\frac{v_{f} - v_{i}}{a}) + \frac{1}{2} \frac{(v_{f}-v_{i})}a^{2}$

(We know that, $(a-b)^{2}=a^{2}+b^{2}-2ab$ )

         $s = (\frac{v_{i}v_{f} - v_{i}v_{i}}{a}) + \frac{1}{2} \frac{(v_{f}^{2} +v_{i}^{2}-2v_{f}v_{i} )}a$

On taking lcm we get,

         $s = \frac{2(v_{i}v_{f} - v_{i}^{2})+(v_{f}^{2} +v_{i}^{2}-2v_{f}v_{i} )}{2a}$

         $s = \frac{2v_{i}v_{f} - 2v_{i}^{2}+v_{f}^{2} +v_{i}^{2}-2v_{f}v_{i} }{2a}$

         $s = \frac{- 2v_{i}^{2}+v_{f}^{2} +v_{i}^{2} }{2a}$

         $s = \frac{- v_{i}^{2}+v_{f}^{2} }{2a}$

(or)    $s = \frac{ v_{f}^{2}-v_{i}^{2} }{2a}$ is the required solution where 't' is eliminated.

         

 (#SPJ2)