Q.

For any arbitrary motion in space, which of the following relations is true

(The average stands for average of the quantity over the time interval t1 to t2)

1 v→average=12[v→(t1)+v→(t2)]  
2 v→average=r→(t2)-r→(t1)t2-t1  
3 v→(t)=v→(0)+a→t  
4 r→(t)=r→(0)+v→(0)t+12a→t2  

Ans.

(2)

The relation (2) is true, others are false because relations (1), (3) and (4) hold only for uniformly accelerated motion.