Kerala KEAM 5 June 2024 Solved Paper

The equation for the motion of the body under constant acceleration is:$$v = u + at$$where:- $v$ is the velocity at time $t$,- $u$ is the initial velocity (which is zero since the body is at rest),- $a$ is the constant acceleration,- $t$ is the time.Therefore, the velocity at time $t$ is:$$v = at$$The power delivered to the body is the rate at which work is done, and it is given by:$$P = Fv$$where:- $P$ is the power,- $F$ is the force acting on the body,- $v$ is the velocity of the body.The force $F$ can be calculated using Newton’s second law:$$F = ma$$where:- $m$ is the mass of the body,- $a$ is the acceleration.Thus, the power delivered to the body is:$$P = ma \cdot v$$Substituting $v = at$ into the equation:$$P = ma \cdot (at) = ma^2t$$Thus, the power is directly proportional to time $t$.$$\boxed{t}$$ Quick Tip: The power delivered to an object under constant acceleration is proportional to the time $t$, because both velocity and force are linearly related to time in such motion.