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Acceleration

The initial v...

Question

The initial velocity of a particle (at $t = 0$ ) is $u$ and the acceleration by $f$ of particle at time $t$ is given $f = a t$ . Where $a$ is a constant which of the following relation for velocity $v$ of particle after time $t$ is correct?

v = u + a t^{2}

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v = u + \frac{a t^{2}}{2}

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v = u + a t

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v = u

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Solution

The correct option is B $v = u + \frac{a t^{2}}{2}$
We know that,
$\frac{d v}{d t} = a$
Hence, here given f=at
$d v = a t d t$
Integrating this and applying the proper limits.
$v - u = a \frac{t^{2}}{2}$
$⟹ v = u + a \frac{t^{2}}{2}$
Hence, option B is correct.

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Similar questions

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

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

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The initial velocity of a particle (at t=0) is u and the acceleration by f of particle at time t is given f=at. Where a is a constant which of the following relation for velocity v of particle after time t is correct?

The correct option is B v=u+at22We know that,dvdt=aHence, here given f=atdv=atdtIntegrating this and applying the proper limits.v−u=at22⟹v=u+at22Hence, option B is correct.

The initial velocity of a particle (at $t = 0$ ) is $u$ and the acceleration by $f$ of particle at time $t$ is given $f = a t$ . Where $a$ is a constant which of the following relation for velocity $v$ of particle after time $t$ is correct?

The correct option is B $v = u + \frac{a t^{2}}{2}$
We know that,
$\frac{d v}{d t} = a$
Hence, here given f=at
$d v = a t d t$
Integrating this and applying the proper limits.
$v - u = a \frac{t^{2}}{2}$
$⟹ v = u + a \frac{t^{2}}{2}$
Hence, option B is correct.