The initial velocity of a particle is u (at t | vedclass

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(B) Given that the acceleration $a(t) = at$ is a function of time.We know that acceleration is the rate of change of velocity,$a = \frac{dv}{dt}$.Ther

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

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(B) Given that the acceleration $a(t) = at$ is a function of time.We know that acceleration is the rate of change of velocity,$a = \frac{dv}{dt}$.Therefore,$dv = a(t) \, dt$.Integrating both sides from initial velocity $u$ at $t = 0$ to final velocity $v$ at time $t$:$\int_{u}^{v} dv = \int_{0}^{t} (at) \, dt$.$[v]_{u}^{v} = a \left[ \frac{t^2}{2} \right]_{0}^{t}$.$v - u = \frac{at^2}{2}$.$v = u + \frac{at^2}{2}$.Thus,the correct relation is $v = u + \frac{at^2}{2}$.

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

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