Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

The initial velocity of a particle is $u$ (at $t = 0$ ) and the acceleration $f$ is given by $at$ . Which of the following relations is valid?

$v = u + at^2$

$v = u + \frac{at^2}{2}$

$v = u + at$

$v = u$

Definition of Acceleration: Acceleration $f$ is defined as the rate of change of velocity with respect to time: $f = \frac{dv}{dt}$ .
Given Condition: The acceleration is given as a function of time: $f = at$ .
Integration: To find the velocity $v$ at time $t$ , we integrate the acceleration function with respect to time: $\int_{u}^{v} dv = \int_{0}^{t} f \, dt = \int_{0}^{t} at \, dt$ Here, the limits of integration for velocity are from initial velocity $u$ to final velocity $v$ , and for time from $0$ to $t$ .
Solving the Integral: $v - u = a \left[ \frac{t^2}{2} \right]_{0}^{t}$ $v - u = \frac{1}{2} at^2$ $v = u + \frac{at^2}{2}$ . Note: The standard equation $v = u + at$ applies only to constant acceleration. Since acceleration here depends on time ( $f \propto t$ ), calculus must be used.

Practice Mode Available

Join thousands of students and practice with AI-generated mock tests.