Kelvi

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

medium

Motion in a Plane

2017

physics

$5$ m/s $^2$

$-4$ m/s $^2$

Explanation

To find the acceleration of the particle at $t = 2$ s, we need to determine the second derivatives of the position functions $x(t)$ and $y(t). \\$ Given: $\\ x = 5t - 2t^2 \\ y = 10t \\$

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

Explanation

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