The x and y coordinates of a particle at a

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The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 7t + 4{t^2}$ and $y = 5t$, where $x$ and $y$ are in metre and $t$ in seconds. The acceleration of particle at $t = 5\;s$ is.........$m/{s^2}$

A

$0$

B

$8$

C

$20$

D

$40$

The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 7t + 4{t^2}$ and $y = 5t$, where $x$ and $y$ are in metre and $t$ in seconds. The acceleration of particle at $t = 5\;s$ is.........$m/{s^2}$

$a = \sqrt {a_x^2 + a_y^2} $

$x=7 t+4 t^{2}$

$\frac{d x}{d t}=7+8 t$

$\frac{d^{2} x}{d t^{2}}=8$

$y=5 t$

$\frac{d y}{d t}=5$

$\frac{d^{2} y}{d t^{2}}=0$

$a_{x}=8$

$a_{y}=0$

$a_{n e t}=\sqrt{8^{2}+0^{2}}$

$=8 m / s^{2}$

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