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A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to

Asked in JEE Main 20th July 2nd Shift 2021; AIEEE 2003 · Motion under constant power

• (1) t^3/2
• (2) t^1/2
• (3) t^3/4
• (4) t^1/4

Step-by-step solution

Why the other options are wrong

• (2) Comes from stopping at the velocity, which goes as t^1/2.
• (3) No single slip gives 3/4; integrating t^1/2 raises the power by one, not by a quarter.
• (4) No single slip gives 1/4; both the speed and the distance grow faster than that.

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