Question

Establish the relation v=u+at​

Answer 1

To prove: v = u + at

Proof:

To prove, let's know some abbreviations,

u = initial velocity

v = final velocity

a = acceleration

t = time taken

As we know that acceleration is the change in velocity (that is, the difference between the final velocity and the initial velocity) with respect to time.

⇒ Acceleration = $\frac{change in velocity}{time taken}$

And, we know, change in velocity = final velocity - initial velocity.

So, Acceleration = $\frac{final velocity- initial velocity}{time taken}$

⇒ a = $\frac{v-u}{t}$

On cross multiplying, we get,

at = v-u

Or, v = u + at.

Hence established.