Question

kinetic energy of a body, moved by a machine is directly proportional to time t. So, distance travelled by the body is proportional to ................ .
(A) t to the power of 3/2
(B) t to the power of 2/3
(C) t to the power of 1/4
(D) t to the power of 1/2

Answer 1

Given,

K.E. ∝ t.

⇒ 1/2 mv² ∝ t

∴ v² ∝ t

⇒ v ∝ √t

∴ S/t ∝ √t

⇒ S ∝ t√t

∴ S  ∝ √(t³)

⇒  $S = t^{\frac{3}{2} }$

Therefore, Option (a). is correct. Distance is directly proportional to t to the power 3/2.

Hope it helps.

Answer 2

Given,

K.E. ∝ t.

⇒ 1/2 mv² ∝ t

∴ v² ∝ t

⇒ v ∝ √t

∴ S/t ∝ √t

⇒ S ∝ t√t

∴ S  ∝ √(t³)

Therefore, Option (a). is correct. Distance is directly proportional to t to the power 3/2.

Hope it helps.