The distance travelled by a body is proportional to the square of time what type of motion

When the distance travelled by a body is directly proportional to the square of the time taken,the motion of the body isgive correct reason to support this answer and also why other options are not correct except correct oneA.uniformB.uniformly acceleratedC.zig zagD.circular

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projectile motionuniform accelerated motionNon uniform accelerated motionnone

Answer : B

Solution : Let x be the distance travelled in time t. Then, <br> `x prop t^(2)` (given) <br> `x = kt^(2)` (Here, k = constant of proportionality) <br> We know that velocity is given <br> `v = (dx)/(dt) = 2 kt` <br> and acceleration is given by <br> `a=(dv)/(dt)=2 k` (constant) <br> Thus, the body has uniform accelerated motion.