Question

The$x$and $y$ coordinates of a particle at any time $t$ are given by $x = 7t + 4t^{2}$ and$y = 5t$, where $x$ and $y$ are in metre and $t$ in seconds. The acceleration of particle at $t = 5$s is

• A. Zero
• B. $8m/s^{2}$
• C. 20 $m/s^{2}$
• D. 40 $m/s^{2}$

Answer 1

Answer: (B)

$8m/s^{2}$

Answer 2

$a = \sqrt{a_{x}^{2} + a_{y}^{2}}$ $= \left\lbrack \left( \frac{d^{2}x}{dt^{2}} \right)^{2} + \left( \frac{d^{2}y}{dt^{2}} \right)^{2} \right\rbrack^{\frac{1}{2}}$

Here$\frac{d^{2}y}{dt^{2}} = 0$. Hence $a = \frac{d^{2}x}{dt^{2}} = 8m/s^{2}$