Question

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 :

• A. $5 m/s^2$
• B. $-4 \, ms^2$
• C. $-8 \, ms^2$
• D. 0

Answer 1

Answer: (B)

$-4 \, ms^2$

Answer 2

$x=5 t-2 t^{2} \,\,\, y=10 t$
$\frac{d x}{d t}=5-4 t \,\,\, \frac{d y}{d t}=10$
$v_{x}=5-4 t \,\,\, v_{y}=10$
$\frac{d v}{d t} x=-4 \,\,\, \frac{d v}{d t} y=10$
$a_{x}=-4\,\,\, a_{y}=0$
Acceleration of particle at $t=2 s$ is $=-4 m / s ^{2}$