Question

The $x$ and $y$ coordinates of a particle at any time t are given by $x= \, 2t+4t^{2}$ and $y= \, 5t$ , where x and y are in metre and t in second. The acceleration of the particle at $t= \, 5 \, s$ is -

• A. $40 \, ms^{- 2}$
• B. $20 \, m \, s^{- 2}$
• C. $8 \, m \, s^{- 2}$
• D. $Zero$

Answer 1

Answer: (C)

Considering the motion of particle in x and y direction.
$v_{x}=\frac{d x}{d t}=2+8t$
And $a_{x}=\frac{d v_{x}}{d t}=8$
$v_{y}=\frac{d y}{d t}=5$
And $a_{y}=\frac{d v_{y}}{d t}=0$
$a=\sqrt{a_{x}^{2} + a_{y}^{2}}$
$a=\sqrt{8^{2} + 0}= \, $ $8 \, m \, s^{- 2}$