The initial velocity of a particle is uleft(r | vedclass

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Question

(c)

$a=\alpha t^{3 / 2}$ (acceleration is a function of time)

$\int \limits_u^v d v=\int \limits_0^t a d t$

$\Rightarrow \int \limits_u^v d v

Vedclass · Accepted Answer

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

Vedclass · Answer

(c)

$a=\alpha t^{3 / 2}$ (acceleration is a function of time)

$\int \limits_u^v d v=\int \limits_0^t a d t$

$\Rightarrow \int \limits_u^v d v=\int \limits_0^t \alpha t^{3 / 2} d t$

$\left.\Rightarrow vight|_u ^v=\left.\alpha \frac{t^{3 / 2}+1}{\frac{3}{2}+1}ight|_0 ^t$

$\Rightarrow (v-u)=\alpha 	imes \frac{2}{5} \quad\left(t^{5 / 2}-0ight)$

$\Rightarrow v-u=\frac{2}{5} \alpha t^{5 / 2}$

$\Rightarrow v=u+\frac{2}{5} \alpha t^{5 / 2}$

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

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