 In this question it's given that the displacement of an object is proportional to square of time and we have to ascertain whether the object moves with uniform velocity, uniform acceleration, increasing acceleration or decreasing acceleration. So in this question we'll be using whatever equation of motions knowledge we have. So let's just write down the first or the equations of motions which we know. And the first equation of motion is given by v is equal to u plus a t where v, let us first write down all the equations and then we'll explain what are the terms in this. And then second equation is s is equal to ut plus half a t squared. And then third equation is v square is equal to u square plus 2 a s where v happens to be final velocity of the object moving in a straight line. So all these equations hold for an object which is moving in a straight line like that. So let's say at t equals to 0 the initial velocity was u and at t equals to t the final velocity is v. This is the distance s or displacement s covered during this time t and it was all through the motion it was moving with a uniform acceleration a. So I'm again writing u is equal to initial velocity s happens to be the displacement, the displacement covered and a is acceleration, acceleration. These three equations hold for uniform acceleration. Now so it's what is the objective of the question it's asking is the displacement of an object is proportional to square of time. So you can clearly see that here by equation number two if you see this you can see s is equal to u t plus half a t square. And this is proportional to square of time if you see s is directly proportional to v square on this question. So hence this is possible only when it is moving with uniform acceleration what was the assumption in this equation the assumption is a is constant only then we can arrive at this particular equation. So hence clearly in this case s is directly proportional to t square so the answer would be b that is uniform acceleration. Now what would be the case in case of uniform velocity if let's say let's explore the option a in case of uniform velocity the in case of uniform velocity my a will be zero so a is zero. So putting a is zero in the second equation I can get s is equal to only u t right which in this case s is directly proportional to t and not t square. This is the case of uniform uniform velocity. So then from through the entire journey the body is moving with uniform velocity u.