The x and y coordinates of a particle at any time t are given by x= 2t+4t2 and y= 5t , where x and y are in metre and t in second. The acceleration of the particle at t= 5 s is -

Question

The x and y coordinates of a particle at any time t are given by x= 2t+4t2 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

Tardigrade Admin · Accepted Answer

Considering the motion of particle in x and y direction. vx=(d x/d t)=2+8t And ax=(d vx/d t)=8 vy=(d y/d t)=5 And ay=(d vy/d t)=0 a=√ax2 + ay2 a=√82 + 0= 8 m s- 2

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

$40 m s^{- 2}$

$20 m s^{- 2}$

$8 m s^{- 2}$

$Z ero$

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

Q. The x and y coordinates of a particle at any time t are given by x=2t+4t2 and y=5t , where x and y are in metre and t in second. The acceleration of the particle at t=5s is -

40ms−2

20ms−2

8ms−2

Zero