Start with the expression for displacement s derived from average velocity and time.

Question

ScanSolve AI Tutor · Accepted Answer

Here is the derivation of the kinematic equation:

Start with the expression for displacement $s$ derived from average velocity and time.
$s = \left(\frac{v+u}{2}\right) \times \left(\frac{v-u}{a}\right)$
Combine the terms into a single fraction.
$s = \frac{(v+u)(v-u)}{2a}$
Expand the numerator using the difference of squares formula, $(x+y)(x-y) = x^2 - y^2$ .
$s = \frac{v^2 - uv + uv - u^2}{2a}$
Simplify the numerator by canceling out the $uv$ terms.
$s = \frac{v^2 - u^2}{2a}$
Multiply both sides by $2a$ to isolate $v^2 - u^2$ .
$2as = v^2 - u^2$
Rearrange the equation to solve for $v^2$ .
$v^2 = u^2 + 2as$
This is the final kinematic equation.

The student's work is ✅ Correct.

Step-by-step solution