(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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Motion in Straight Line

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Uniformly Accelerated Motion

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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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The position of a particle moving along the $x$ axis is given by the equation $x = (10 + 6t - 3t^2) \ m$. The distance travelled by the particle from $t = 1 \ s$ to $t = 4 \ s$ is: (in $m$)

If a body loses half of its velocity on penetrating $3 \, cm$ in a wooden block,then how much will it penetrate more before coming to rest? (in $cm$)

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