Question

prove that v= u+at i was able to prove the other formulas but not this one

Answer 1

Given:

• To prove v = u + at .

Proof:

We will be using graphical method to prove the first equation of motion which is v = u + at

Now we know that slope of a velocity - time graph gives acceleration .

And also Slope = tan∅ .

From the above ( v - t ) graph ,

☞Slope = tan ∅ = perpendicular/base = BC/AB.

Now in the graph

• BC = ∆v = ( v - u ).
• AB = t .

So , on putting these values ,

$\sf{\implies slope = tan\theta }$

$\sf{\implies slope = \dfrac{BC}{AB}}$

$\sf{\implies slope = \dfrac{v-u}{t}}$

$\sf{\implies accel^{n}=\dfrac{v-u}{t}}$

$\sf{\implies a=\dfrac{v-u}{t}}$

$\sf{\implies at = v - u}$

$\red{\bf{\leadsto v = u + at}}$

Hence proved.