(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

$A$ car moving along a straight highway with a speed of $126 \; km/h$ is brought to a stop within a distance of $200 \; m$. How long (in $seconds$) does it take for the car to stop?

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If the displacement of an object moving along a straight line is proportional to the square of the time elapsed,does the object have a constant velocity or a constant acceleration?

Medium

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$A$ car is moving along a straight road with uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance $s$ with velocities $30\; km/h$ and $40\; km/h$ respectively. Find the velocity of the car midway between $P$ and $Q$.

MediumAIPMT 1988

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$A$ truck moving with a constant velocity $12 \,m/s$ crosses a car moving from rest with uniform acceleration $2 \,m/s^2$. The distance the car has to travel from the starting point to cross the truck again is (in $\,m$)

EasyAP EAMCET 2023

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$A$ graph between the square of the velocity of a particle and the distance $s$ moved by the particle is shown in the figure. The acceleration of the particle is $...........m/s^2$.

Medium

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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?

Similar Questions

$A$ car moving along a straight highway with a speed of $126 \; km/h$ is brought to a stop within a distance of $200 \; m$. How long (in $seconds$) does it take for the car to stop?

If the displacement of an object moving along a straight line is proportional to the square of the time elapsed,does the object have a constant velocity or a constant acceleration?

$A$ car is moving along a straight road with uniform acceleration. It passes through two points $P$ and $Q$ separated by a distance $s$ with velocities $30\; km/h$ and $40\; km/h$ respectively. Find the velocity of the car midway between $P$ and $Q$.

$A$ truck moving with a constant velocity $12 \,m/s$ crosses a car moving from rest with uniform acceleration $2 \,m/s^2$. The distance the car has to travel from the starting point to cross the truck again is (in $\,m$)

$A$ graph between the square of the velocity of a particle and the distance $s$ moved by the particle is shown in the figure. The acceleration of the particle is $...........m/s^2$.

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