When the distance travelled by a body is directly proportional to the square of the time taken,the motion of the body is(give correct reason to support this answer ) and also why other options are not correct except correct one

A.uniform

B.uniformly accelerated

C.zig zag

D.circular

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Solution

It is given that the distance is directly proportional to the square of time.
Which implies
let s be distance, t be the time, v be the velocity and a be the acceleration $s space alpha space t squared l e t space k space b e space t h e space c o n s tan t space o f space p r o p o r t i o n a l i t y space s space equals space k t squared d i f f e r e n t i a t i n g space w i t h space r e s p e c t space t o space t i m e space w e space g e t space t h e space v e l o c i t y fraction numerator d s over denominator d t end fraction space equals space v space equals space space 2 k t d i f f e r e n t i a t i n g space v e l o c i t y space w i t h space r e s p e c t space t o space t i m e space w e space g e t space a c c e l e r a t i o n fraction numerator d v over denominator d t end fraction space equals space a space equals space 2 k$
Hence we get a constant value of acceleration.
So the motion of the body is uniformly accelerated.
Hsnce the answer is option (B).

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