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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 = 2 s is
Explanation
Differentiate twice: $a_x = -4$, $a_y = 0$ at all times.
Detailed Solution
$x = 5t - 2t^2$, $y = 10t$
$v_x = \frac{dx}{dt} = 5 - 4t$, $v_y = \frac{dy}{dt} = 10$
$a_x = \frac{dv_x}{dt} = -4$, $a_y = \frac{dv_y}{dt} = 0$
Acceleration of the particle at t = 2 s is $-4\ m/s^2$.