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Acceleration

What distance...

Question

What distance will it traverse before it stops?

(\frac{3}{2 a}) {v_{0}}^{\frac{3}{2}}

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(\frac{2}{3 a}) v_{0}^{\frac{3}{2}}

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(\frac{3}{2 a}) v_{0}^{\frac{2}{3}}

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(\frac{2}{5 a}) v_{0}^{\frac{3}{2}}

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Solution

The correct option is A $(\frac{2}{3 a}) v_{0}^{\frac{3}{2}}$
$ω = - a \sqrt{v},$ minus sign for deceleration
$v \frac{d v}{d x} = - a \sqrt{v}$
Integrating, $\int_{v_{0}}^{0} v^{1 / 2} d v = - a \int_{0}^{x_{0}} d x x_{0} = \frac{2 {v_{0}}^{3 / 2}}{3 a}$

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A train is moving with a velocity of 400 m/s with the application of brakes, retardation of $10 m s^{- 2}$ is produced. Calculate the following:

1) after how much time will it stop.

2) how much distance will it cover before it stops.

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