Question

obtain the velocity-time equation by graphical method ​

Answer 1

Answer:

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

=Change in velocityTime taken

⇒

a

=

v

−

u

t

⇒a=v-ut

⇒

a

=

O

C

−

O

D

t

=

D

C

t

⇒a=OC-ODt=DCt

⇒

a

t

=

D

C

⇒at=DC

-----(ii)

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

v

=

a

t

+

u

v=at+u

⇒

v

=

u

+

a

t

⇒v=u+at

Explanation: