Question

what type of motion the body has if the distance travelled by a body is directly proportional to the square of time taken?

Answer 1

If the distance travelled by a body is directly proportional to the square of time taken, then the body is travelling with constant Acceleration. as acc= distance/time square
hence in constant acceleration the distance is directly proportional to the square of time taken.

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Answer 2

it is given that , s(displacement)=kt^2 (here k is a constant)
then after differentiating it wrt time we get acceleration that is equal to k (ie, acceleration is constant).
hence it is uniformly accelerated motion.