The $x$ and $y$ coordinates of the particle at any time are $x=5 t-2 t^{2}$ and $y=10 t$ respectivel

Question

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 metres and $t$ in seconds. The acceleration of the particle at $t=2 \mathrm{~s}$ is\

Professor PC Thomas Classes · Answer

(b) : $x=5 t-2 t^{2}, y=10 t$\ $\frac{d x}{d t}=5-4 t, \frac{d y}{d t}=10 \quad 	herefore \quad v_{x}=5-4 t, v_{y}=10$\ $\frac{d v_{x}}{d t}=-4, \frac{d v_{y}}{d t}=0 \quad 	herefore a_{x}=-4, a_{y}=0$ Acceleration, $\vec{a}=a_{x} \hat{i}+a_{y} \hat{j}=-4 \hat{i}$\ $	herefore \quad$ The acceleration of the particle at $t=2 \mathrm{~s}$ is $-4 \mathrm{~m} \mathrm{~s}^{-2}$.\