Question

Distance travelled by the body is directly proportional to time. Is there any external force acting on it ?

Answer 1

yes....
Distance=Speed  *  Time
....
and Distance is proportional to Time it is only possible when there is a constant speed......
for which a force is needed..
suppose you are pulling an object kept at  the table ...with a  force.......such that its speed remains same then....  
Distance is proportional to Time
..
cheers!!!

Answer 2

By the second equation of motion,

s = ut + 1/2 at^2

S is directly proportional to the time only when there is no external force acting on it.

In the absence of external force, acceleration ‘a’ of the object becomes zero and the equation of motion becomes

s= ut

Since acceleration is zero so speed ‘u’ of the object remains constant.

Hence, it can be concluded that S is directly proportional to t.