Question

derive the equation of motion v=u+at graphically​

Answer 1

Answer :-

Let an object is moving with uniform acceleration

Let the initial velocity of the object = u

Let the object is moving with uniform acceleration, a.

Let object reaches at point B after time, t and its final velocity becomes, v

Draw a line parallel to x-axis DA from point, D from where object starts moving.

Draw another line BA from point B parallel to y-axis which meets at E at y-axis.

Let OE = time, t

______________________________

Now, from the graph,

BE = AB + AE

⇒ v = DC + OD (Since, AB = DC and AE = OD)

⇒ v = DC + u (Since, OD = u)

⇒ v = DC + u ------------------- (i)

$now \: acceleration \:(a)\: = \frac{change \: in \: velocity \: \: }{time \: taken \: } \\ = > a = \frac{v - u}{t} \\ = > a = \frac{OC - OD}{t} = \frac{DC}{t}$

⇒ at = DC -----(ii)

By substituting the value of DC from (ii) in (i) we get,

⇒ v = at + u

⇒ v = u + at

Above equation is the relation among initial velocity (u),final velocity (v), acceleration (a) and time (t). It is called first equation of motion.

graph is in the attachment.

Hope it will help uh..