Question

derive the equations of motion by graphical method

Answer 1

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Answer 2

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Let an object is moving with uniform acceleration.

Velocity Time Graph

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)

=

Change in velocity

Time taken

⇒

a

=

v

−

u

t

⇒

a

=

O

C

−

O

D

t

=

D

C

t

⇒

a

t

=

D

C

-----(ii)

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

v

=

a

t

+

u

⇒

v=u+at

Above equation is the relation among initial vlocity (

u

), final velocity (

v

), acceleration (a) and time (t). It is called first equation of motion.

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