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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
Explanation
Given: $x = 5t - 2t^{2}$ $v_{x} = dx/dt = 5 - 4t$ $y = 10t$; $a_{x} = dv_{x}/dt = -4$; $v_{y} = dy/dt = 10$ $\vec{a} = a_{x}i + a_{y}j$; $\vec{a} = -4i m/s^{2}$; $a_{y} = dv_{y}/dt = 0$ Hence, acceleration of particle at $(t = 2s) = -4 m/s^{2}$