Question

Using the concept of distance time graph derive the relation v=u+at.

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

⇒

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

+

a

t