Question

Hi!



Derive the equation v = u + at​

Answer 1

Answer:

Explanation:

In the above graph,

The velocity of the body changes from A to B in time t at a uniform rate.

BC is the final velocity and OC is the total time t.

A perpendicular is drawn from B to OC, a parallel line is drawn from A to D, and another perpendicular is drawn from B to OE (represented by dotted lines).

Following details are obtained from the graph above:

The initial velocity of the body, u = OA

The final velocity of the body, v = BC

From the graph, we know that

BC = BD + DC

Therefore, v = BD + DC

v = BD + OA (since DC = OA)

Finally,

v = BD + u (since OA = u) (Equation 1)

Now, since the slope of a velocity-time graph is equal to acceleration a,

So,

a = slope of line AB

a = BD/AD

Since AD = AC = t, the above equation becomes:

BD = at (Equation 2)

Now, combining Equation 1 & 2, the following is obtained:

v = u + at

Answer 2

Explanation :

➤ First equation of motion :-

• ${v = u + at}$

We know,

$acceleration = \frac{change\;in\;velocity}{time\;taken}$

We know,

$change\;in\;velocity = final\;velocity - initial\;velocity$

Where,

final velocity = v

initial velocity = u

time = t

acceleration = a

Again,

$acceleration = \frac{v\;-u}{t}$

$a = \frac{v\;-u}{t}$

Cross multiply,

$at = v\;-u$

$v = u\;+at$

Hence, derived !