An object is moving with a uniform acceleration . . .

Question : An object is moving with a uniform acceleration. Its velocity after 5 seconds is 25 m/s and after 8 seconds s 34 m/s. Find the distance travelled by the object in 10th second.

Doubt by Yana 

Solution : 

Let initial velocity of the object be 'u' and uniform acceleration be 'a'

We know, 

v=u+at

Case I :
t=5 sec
v=25 m/s

v=u+at 
25=u+a(5) 

25=u+5a — (1) 

Case II : 
t=8 sec
v=34 m/s 

v=u+at 
34=u+a(8) 

34=u+8a — (2)

Solving equation (1) and (2) 

34=u+8a

25=u+5a
-     -  - 
-----------------
9 = 0 + 3a
-----------------

3a=9
a=9/3
a=3 m/s²

putting in equation (1) 

25=u+5(3)
25=u+15
25-15=u
10=u
u=10 m/s

We know, distance covered by a body in nth second is given by 

The distance travelled by the object in 10th second is 38.5 m