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Acceleration in 2D

The coordinat...

Question

The coordinates of a moving particle at any time $^{'} t^{'}$ are given by $x = t^{3}$ and $y = 4 t^{2}$ , where $x$ and $y$ are in metre and $t$ in second. The acceleration of the particle at time $t = 1 s$ is given by

6 {ms}^{- 2}

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8 {ms}^{- 2}

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10 {ms}^{- 2}

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14 {ms}^{- 2}

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Solution

The correct option is C $10 {ms}^{- 2}$
$x = t^{3}, v_{x} = 3 t^{2}, a_{x} = 6 t$
$∴ a_{x} (t = 1 s) = 6 {m/s}^{2}$

$y = 4 t^{2}, v_{y} = 8 t, a_{y} = 8 {m/s}^{2}$ ,
$a = \sqrt{a_{x}^{2} + a_{y}^{2}} = \sqrt{6^{2} + 8^{2}}, a = 10 {m/s}^{2}$
$∴$ (c)

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Similar questions

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The coordinates of a moving particle at any time 't' are given by x= ∝t³ and y=βt³. The speed of the particle at time 't' is

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The coordinates of a moving particle at any time ′t′ are given by x=t3 and y=4t2, where x and y are in metre and t in second. The acceleration of the particle at time t=1 s is given by

The correct option is C 10 ms−2x=t3, vx=3t2, ax=6t ∴ax(t=1s)=6 m/s2 y=4t2,vy=8t, ay=8 m/s2, a=√a2x+a2y=√62+82, a=10 m/s2 ∴ (c)

The coordinates of a moving particle at any time $^{'} t^{'}$ are given by $x = t^{3}$ and $y = 4 t^{2}$ , where $x$ and $y$ are in metre and $t$ in second. The acceleration of the particle at time $t = 1 s$ is given by

The correct option is C $10 {ms}^{- 2}$
$x = t^{3}, v_{x} = 3 t^{2}, a_{x} = 6 t$
$∴ a_{x} (t = 1 s) = 6 {m/s}^{2}$

$y = 4 t^{2}, v_{y} = 8 t, a_{y} = 8 {m/s}^{2}$ ,
$a = \sqrt{a_{x}^{2} + a_{y}^{2}} = \sqrt{6^{2} + 8^{2}}, a = 10 {m/s}^{2}$
$∴$ (c)