Q92 / 180 · NEET 2017 · Physics

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 $t$ is in seconds. The acceleration of the particle at $t = 2 s$ is

A
$0 m s^{- 2}$
B
$5 m s^{- 2}$
Correct answer
C
$- 4 m s^{- 2}$
D
$- 8 m s^{- 2}$

Solution

$\begin{matrix} x = 5 t - 2 t^{2} & y = 10 t \end{matrix}$

$\begin{matrix} \frac{d x}{d t} = 5 - 4 t & \frac{d y}{d t} = 10 \end{matrix}$

The velocity of the particle in $x$ and $y$ coordinate is

$\begin{matrix} v_{x} = 5 - 4 t & v_{y} \end{matrix} = 10$

$\frac{d v_{x}}{d t} = - 4$ $\frac{d v_{y}}{d t} = 10$

$\begin{matrix} a_{x} = - 4 & a_{y} = 0 \end{matrix}$

Acceleration of particle at $t = 2 s$ is $= - 4 m / s^{2}$

Hence, the correct answer is option: 'C'.

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

Solution

Relevant 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 $t$ is in seconds. The acceleration of the particle at $t = 2 s$ is