obtain the velocity-time equation by graphical method
Answers
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: