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Acceleration

The x and y c...

Question

The x and y coordinates of the particle at any time are $x = 5 t - 2 t^{2}$ and $y = 10 t$ respectively, where x and y are in meters and t in seconds. The acceleration of the particle at $t = 2 s$ is

0

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5 m / s^{2}

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- 4 m / s^{2}

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- 8 m / s^{2}

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Solution

The correct option is C $- 4 m / s^{2}$

First, differentiate the $x - c o o r d i n a t e$ with respect to $t$ , two times we will get it $- 4$ , its nothing but acceleration in $x$ $d i r e c t i o n$ .
And the double derivative of $y$ coordinate is $z e r o$ so acceleration in y-direction is $z e r o$ .

So net acceleration is $- 4 m / s^{2}$

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Similar questions

The $x$ and $y$ coordinates of the particle at any time are $x = 5 t - 2 t^{2}$ and $y = 10 t$ respectively, where $x$ and $y$ are in meters and $t$ in seconds. The acceleration of the particle at $t = 2 s$ is

Q. The

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x = 5 t - 2 t^{2}

and

y = 10 t

respectively, where

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m e t e r s

and

t

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The acceleration of the particle at

t = 2 s

Q. The x and y coordinates of a particle at any time

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The x and y coordinates of the particle at any time are x=5t−2t2 andy=10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t=2s is

The correct option is C −4m/s2First, differentiate the x−coordinate with respect to t , two times we will get it −4, its nothing but acceleration in x direction.And the double derivative of y coordinate is zero so acceleration in y-direction is zero .So net acceleration is −4m/s2

The x and y coordinates of the particle at any time are $x = 5 t - 2 t^{2}$ and $y = 10 t$ respectively, where x and y are in meters and t in seconds. The acceleration of the particle at $t = 2 s$ is