(C) Given,acceleration $a = \frac{dv}{dt} = \alpha t^{3/2}$.Integrating both sides with respect to time $t$ from $0$ to $t$:$\int_{u}^{v} dv = \int_{0

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$v=u+\frac{2}{5}\alpha t^{5/2}$

(C) Given,acceleration $a = \frac{dv}{dt} = \alpha t^{3/2}$.Integrating both sides with respect to time $t$ from $0$ to $t$:$\int_{u}^{v} dv = \int_{0}^{t} a dt$$\int_{u}^{v} dv = \int_{0}^{t} \alpha t^{3/2} dt$$[v]_{u}^{v} = \alpha \left[ \frac{t^{3/2 + 1}}{3/2 + 1} \right]_{0}^{t}$$v - u = \alpha \left[ \frac{t^{5/2}}{5/2} \right]_{0}^{t}$$v - u = \frac{2}{5} \alpha t^{5/2}$$v = u + \frac{2}{5} \alpha t^{5/2}$

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

Medium

The initial velocity of a particle is $u$ at $t=0$ and the acceleration $a$ is given by $a = \alpha t^{3/2}$. Which of the following relations is valid?

A
$v=u+\alpha t^{3/2}$
B
$v=u+\frac{3}{2}\alpha t^3$
C
$v=u+\frac{2}{5}\alpha t^{5/2}$
D
$v=u+\alpha t^{5/2}$

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Class 11

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Chapter

Motion in Straight Line

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Uniformly Accelerated Motion

For a moving body at any instant of time,which of the following statements is correct?

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An object accelerates from rest to a velocity $27.5 \,m/s$ in $10 \,s$. Find the distance covered by the object in the next $10 \,s$ (in $m$).

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$A$ body lying initially at point $(3,7)$ starts moving with a constant acceleration of $4 \hat{i}$. Its position after $3 \,s$ is given by the coordinates ..........

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$A$ particle moves in a straight line and its position $x$ at time $t$ is given by $x^2 = 2 + t$. Its acceleration is given by

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The velocity $v$ of a particle as a function of its position $x$ is expressed as $v = \sqrt{c_1 - c_2 x}$,where $c_1$ and $c_2$ are positive constants. The acceleration of the particle is

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The initial velocity of a particle is $u$ at $t=0$ and the acceleration $a$ is given by $a = \alpha t^{3/2}$. Which of the following relations is valid?

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For a moving body at any instant of time,which of the following statements is correct?

An object accelerates from rest to a velocity $27.5 \,m/s$ in $10 \,s$. Find the distance covered by the object in the next $10 \,s$ (in $m$).

$A$ body lying initially at point $(3,7)$ starts moving with a constant acceleration of $4 \hat{i}$. Its position after $3 \,s$ is given by the coordinates ..........

$A$ particle moves in a straight line and its position $x$ at time $t$ is given by $x^2 = 2 + t$. Its acceleration is given by

The velocity $v$ of a particle as a function of its position $x$ is expressed as $v = \sqrt{c_1 - c_2 x}$,where $c_1$ and $c_2$ are positive constants. The acceleration of the particle is

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